Course: 201A Mathematics A III

Lecturer: prof. dr hab. Jan Blinowski

Semester: winter

Lecture hours per week: 4

Class hours per week: 4

Code: 11.103201A

Credits: 10

1. Linear differential equations.
2. Rieman integral of many variable functions.
3. Surface integrals.
4. Extrema with boundary conditions.
5. Holomorphic functions: elementary definitions and properties.

Note: Lecture is dedicated to BSc students.

1. W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach.
2. F. Leja, Rachunek różniczkowy i całkowy.
3. M. Grabowski, Analiza matematyczna.
4. E. Karaśkiewicz, Zarys teorii wektorów i tensorów.
5. G. Fichtencholz, Rachunek różniczkowy i całkowy.

Mathematics A (semester I and II).

Pass of class exercises, written and oral examination.

Course: 201B Mathematical analysis B III

Lecturer: dr hab. Wiesław Pusz

Semester: winter

Lecture hours per week: 4

Class hours per week: 4

Code: 11.103201B

Credits: 10

The third part of the mathematical analysis course. The aim of the course is to supply the basic theoretical information and to present the basic methods for.

• solving systems of the first order ordinary differential equations (systems of linear differential equations with constant coefficients in particular)
• solving higher order differential equations
• investigating functions on surfaces (extrema of function on surface)
• evaluating multiple integrals (Fubini Theorem, changing variables)
• evaluating integrals depending on parameters
• evaluating integrals over surfaces (arc length of a curve, area of a surface, elements of the theory of differential forms, Stokes formula, scalar and vector potentials)
• investigating functions of a complex variable (holomorphic functions, classification of singular points, evaluating contour integrals)

1. F. Leja, Rachunek różniczkowy i całkowy.
2. F. Leja, Funkcje zespolone.
3. W. Rudin, Podstawy analizy matematycznej.
4. K. Maurin, Analiza cz.1 – Elementy.
5. K. Kuratowski, Wstęp do teorii mnogości i topologii.

Mathematical analysis I, II (B lub C), Algebra.

Pass of class exercises, written and oral examination.

Course: 201C Mathematical analysis C III

Lecturer: prof. dr hab. Paweł Urbański

Semester: winter

Lecture hours per week: 4

Class hours per week: 4

Code: 11.103201C

Credits: 10

1. Analysis on submanifolds of affine spaces: tangent vectors and covectors, Lagrange multipliers, differential forms and densities, orientation of submanifolds, integration of forms and densities, Stokes theorem, vector analysis.
2. The theory of analytical functions: analytic and holomorphic functions, Cauchy formulae, analytic prolongation, multivalued functions, singularities of analytical functions, residua – theory and applications, meromorphic functions.
3. Theory of generalised functions (distributions): elementary operations on distributions, convolution of functions and distributions, the Fourier transformation, equations in the space of distributions, periodic distributions, Fourier series.

Lecture notes will be available in November 1998.

1. L. Schwartz, Kurs analizy matematycznej.
2. K. Maurin, Analiza cz.2.
3. M. Spivak, Analiza na rozmaitościach.
4. L. Schwartz, Metody matematyczne w fizyce.

Mathematical analysis C I and C II.

Oral and written examination.

Course: 202A Physics A III - Vibrations and Waves

Lecturer: prof. dr hab. Michał Nawrocki

Semester: winter

Lecture hours per week: 4

Class hours per week: 4

Code: 13.203202A

Credits: 10

This is a simpler version of a traditional course. Its main goals are to provide students with the opportunity to acquire an intuition for the physical effects and to resolve simple physical problems. This course places significant emphasis on lecture demonstration and on the relation between the course material and everyday life.

1. Vibrations

Free, damped and forced harmonic vibrations. Resonance.

Non-linear vibrations.

Self-induced vibrations;

Parametric resonance.

Coupled vibrations;

2. Waves.

Wave motion.

Elastic waves.

Electromagnetic waves.

Wave optics.

Geometrical optics.

Light polarisation.

Absorption, dispersion, scattering.

1. R. Resnick, D. Halliday, Fizyka I.
2. D. Halliday, R. Resnick, Fizyka II.
3. I.W.Sawieliew, Wykłady z fizyki, t.I i II.
4. S. Pieńkowski, Fizyka doświadczalna-optyka.
5. Sz. Szczeniowski, Fizyka doświadczalna-optyka.
6. Januszajtis, Fizyka dla politechnik – fale.
7. J. Orear, Fizyka, WNT 1990.
8. J. Ginter, Fizyka III, t.I i II, skrypt dla NKF.
9. Lecture notes.

Physics I and II, Mathematics I and II.

The final exam consists of two parts: written and oral. The written part is open for students who obtained a better score than 50% for each part (test and problems) of colloquia 1 and/or 2.

The oral part is open for students who: a) obtained a better score than 50% for each part of colloquia 1 and 2 and participated in the written part of the final exam, or b) obtained a better score than 50% for each part of colloquia 1 or 2 and the written part of the final examination.

Course: 202B Physics B III – Waves and oscillations

Lecturer: prof. dr hab. Andrzej K. Wróblewski

Semester: winter

Lecture hours per week: 4

Class hours per week: 4

Code: 13.203202B

Credits: 10

The course deals mainly with oscillations and waves with special stress on the physics of electromagnetic waves in the visible region of the spectrum, i.e. optics. Similarity of the mathematical formalism in description of various oscillations and waves (i.e. harmonic oscillator equation or classical wave equation) makes it possible to consider jointly all oscillations and waves (mechanical, acoustic, visible light).

The course is divided into following parts:

1. Oscillations of systems with one degree of freedom (mathematical and physical pendulum, damped oscillations, forced oscillations, RLC circuits, addition of oscillations).
2. Oscillations of systems with many degrees of freedom (coupled pendulums, coupled circuits, mechanical and electric filters, oscillations of continuous systems (strings, rods), Fourier analysis of oscillations).
3. Waves (wave equation, phase and group velocity, Doppler effect, surface water waves, pressure waves in rods, acoustic waves, reflection, refraction, and total internal reflection of waves, wave packets).
4. Electromagnetic waves (prediction from Maxwell equations, plane waves, dipole radiation, energy and momentum of electromagnetic waves – the Poynting vector, reflection and refraction of electromagnetic waves (Fresnel formulae), dispersion, polarisation of light due to its scattering, propagation of electromagnetic waves in anisotropic media (elements of crystal optics), retarding plates, chromatic polarisation, birefringence forced mechanically, electrically (Kerr effect), and magnetically (Cotton-Mouton effect), rotation of polarisation plane (Faraday effect)).
5. Interference and diffraction (interference of waves from two and more than two sources, interference of light in thin plates, Fraunhofer diffraction, diffraction grating, Fresnel diffraction, elements of atmospheric optics (rainbow, halo), interference and diffraction of particle beams).

The course deals almost entirely with the classic theory. Only at the very end the diffraction and interference of matter waves (electrons, neutrons) is shortly discussed.

Literature:

No single textbook corresponds strictly to the material presented in this course.

1. Sz. Szczeniowski - Fizyka doświadczalna, tom IV – Optyka.
2. J. Ginter - Fizyka fal (cz. 1 i 2).
3. Crawford: Waves and Oscillations (Volume 3 of the Berkeley Course of Physics)

may be used as an auxiliary source.

Physics I, Physics II, I Physics Laboratory.

Pass of class exercises, written and oral examination.

Course: 203 Physics laboratory I (a)

Head: dr hab. Tomasz Morek

Semester: winter

Lecture hours per week: 0

Class hours per week: 3

Code: 13.202203

Credits: 3,5

Laboratory program includes 10 exercises (amounts depends on number of weeks in the semester) from mechanics, heat, electricity, optics and nuclear physics. The aim of these experiments is to teach students elementary experimental methods through simple exercises, which demand in manual cleverness, and to learn analysis of experimental data.

1. Source information about exercises is included in special instructions (which are available in the secretariat of the Laboratory) and in the following text-books:
2. H.Szydłowski, Pracownia fizyczna
3. A.Zawadzki, H.Hofmokl, Laboratorium fizyczne
4. F.Kohlraush, Fizyka laboratoryjna (in special cases)

Before the beginning of the laboratory work students should get acquianted with rules of the analysis of experimental results. The following books are helpful:

1. J.R.Taylor, Wstęp do analizy błędu pomiarowego
2. G.L.Squires, Praktyczna fizyka
3. H.Abramowicz, Podstawy rachunku błędów
4. H.Hansel, Podstawy rachunku błędów
5. P.Jaracz, Podstawy rachunku błędu pomiarowego (preliminary version)

Principles of experimental error analysis.

Introduction to techniques of measurements and preliminary laboratory.

10 experiments with pass-grades.

Course: 204 Physics laboratory I (b)

Head: dr hab. Tomasz Morek

Semester: summer

Lecture hours per week: 0

Class hours per week: 3

Code: 13.203204

Credits: 4

Laboratory program includes 10 exercises (the exact number depends on number of weeks in the semester) from mechanics, heat, electricity, optics and nuclear physics. The aim of these experiments is to teach students elementary experimental methods through simple exercises, which demand in manual , and to learn analysis of experimental data.

I Physics Laboratory (a).

10 experiments with pass-grades.

Course: 205 Physics IV – Introduction to modern physics

Lecturer: prof. dr hab. Jan Królikowski

Semester: summer

Lecture hours per week: 2

Class hours per week: 2

Code: 13.204205

Credits: 5

1. Wave-particle dualism.

1. Black body radiation. Rayleigh–Jeans theory, Planck equation.
2. Photoelectric effect, X–ray, Compton effect.
3. Emission and absorption spectra. Bohr model of atom, ionisation energy, Franck–Hertz experiment.
4. Diffraction and interference of photons and microparticles. Heisenberg uncertainty principle, de Broglie hypothesis. Wave function, phase and group velocity.

2. Schrödinger equation.

1. Step potential, barrier potential, tunnelling effect. Scanning tunnelling microscope.
2. Bound states: one–dimensional quantum well, finite and infinitive.
3. Operators in quantum mechanics. Eigenstates eigenvectors. Observable. Orbital momentum operator, spherical functions.
4. Hydrogen atom.

3. Atomic and molecular spectra.

1. Zeeman effect, Stark effect, spin–orbit coupling. Many electron atoms. Pauli exclusion principle, selection rules.
2. Molecular spectra.

4. Quantum statistics.

1. Bose Einstein statistics, photon gas, Fermi–Dirac statistics, electron gas.

5. Elements of solid state physics.

1. Band theory, p-n junction, transistor.

1. H. A. Enge, M. R. Wehr, J. A. Richards, Wstęp do fizyki atomowej.
2. I. W. Sawieliew, Wykłady z fizyki, t. 3.
3. Sz. Szczeniowski, Fizyka doświadczalna, cz. V.

Physics I, II, III, Mathematics.

Pass of class exercises, examination.

Course: 206 Mathematical methods of physics (a)

Lecturer: prof. dr hab. Jacek Tafel

Semester: summer

Lecture hours per week: 3

Class hours per week: 3

Code: 11.103206

Credits: 7,5

1. Basic definitions of group theory.
2. Point groups.
3. Group representations and character theory.
4. Lie algebras.
5. Elements of differential geometry.
6. Lie groups and their algebras.
7. Important properties of Lie group representations.
8. Lie groups in physics.

1. A Trautman, Grupy i ich reprezentacje (lecture notes).
2. A.I. Kostrykin, Wstęp do algebry.
3. M Hamermesh, Teoria grup w zastosowaniu do zagadnień fizycznych.

Mathematical analysis, Algebra and geometry.

Pass of class exercises, examination.

Course: 207 Mathematical methods of physics (b) (Introduction to theory of special functions)

Lecturer: dr hab. Jan Dereziński

Semester: summer

Lecture hours per week: 3

Class hours per week: 3

Code: 11.103207

Credits: 7,5

The course is devoted to the theory of the most elementary special functions and related mathematical concepts.

1. Additional material on complex analysis

2. The Gamma function (the Euler integrals, infinite products, the saddle point method used to derive the Stirling formula, the asymptotic expansion of the Gamma function).

3. Differential equations in a complex domain.

4. The Bessel equation, the Bessel, Hankel and Neumann functions, the separation of variable in the Helmholz equation.

5. Elements of the theory of Hilbert spaces, orthonormal bases, projections.

6. Orthogonal polynomials - general theory.

7. Classical orthogonal polynomials (in particular, the Hermit, Tchebyshev and Legendre polynomials).

8 Spherical harmonics.

1. E. Whittaker, G. Watson, Analiza Współczesna.
2. Lecture notes

Mathematical Analysis B or C.

Pass of class exercises, written and oral examination.

Course: 209A Modern theoretical mechanics

Lecturer: dr Zygmunt Ajduk

Semester: summer

Lecture hours per week: 3

Class hours per week: 3

Code: 13.203209A

Credits: 7,5

1. Nonrelativistic mechanics of many particles systems

Motion and its relativity. Principles of dynamics, Galileo principle of relativity, conservation laws. Motion in electromagnetic field and in central conservative forces. Constraints, Lagrange equations of the first and second kind. Equilibrium position and small oscillations.

2. Nonrelativistic mechanics of rigid bodies.

Motion of rigid bodies, physical pendulum, free and heavy symmetric tops.

3. Analytical mechanics.

Hamilton principle, Noether theorem. Hamilton canonical equations, Poisson brackets, general equation of mechanics, Poisson-Jacobi equation. Deterministic chaos, atractors, bifurcations.

4. Relativistic mechanics.

Special Lorentz transformation, Einstein principle of relativity, principles of dynamics, Hamilton principle, motion in electromagnetic field.

1. W. Rubinowicz, W. Królikowski, Mechanika teoretyczna.
2. G. Białkowski, Mechanika klasyczna.
3. L. Landau, E. Lifszyc, Mechanika.

Prerequisites:

Pass of class exercises, written and oral examination.

Course: 209B Classical mechanics

Lecturer: prof. dr hab. Wojciech Kopczyński

Semester: winter and summer

Lecture hours per week: 2

Class hours per week: 2

Code: 13.203209B

Credits: 10

1. Kinematics

Time, space, a material point. The Einstein summation convention. The velocity and the acceleration. The triad of Frenet, the decomposition of acceleration onto the tangent and normal components. The flat motion, its complex description, the radial and transversal components of velocity and acceleration. Geometry and kinematics of the rotations, the angular velocity, comparison of motion with respect to two different frames of reference.

2. Principles of Newtonian dynamics

Analysis of the I-st and the II-nd principle of dynamics from the historical and contemporary point of view.

3. Elements of variational calculus

Formulation of the problem, the Euler-Lagrange equations. The brachistochrone. The first integrals of the Euler-Lagrange equations. The conditional extrema.

4. The equations of mechanics as a variational problem

Without the constraints, the equations of mechanics are example of the Euler-Lagrange equations. Arbitrariness of co-ordinates. Incorporation of the constraints. The first integrals of the Lagrange equations.

5. The symmetries and the conservation laws, the Noether theorem

The definition of symmetries. The variations with the time variation. The Noether identity. The transformations of the Galilei group as symmetries of mechanics. The Lorentz group and the relativistic lagrangian.

6. One-dimensional problems

The discussion of one-dimensional motion. The period of the motion, isochronism. The harmonic oscillator. The flat pendulum. The isochronic pendulum. The parametric resonance.

7. Small vibrations of systems with many degrees of freedom

Motion near equilibrium. The normal frequencies and co-ordinates. The three-dimensional oscillator and its dynamical symmetry.

8. The motion under the influence of the central force

The general discussion of the motion under the influence of the central force. The Kepler problem. The dynamical symmetry in the Kepler problem.

9. The rigid body

The definition of the rigid body. The two frames of reference connected with a rigid body. The angular velocity. The Euler angles. The kinetic energy and the tensor of inertia. The properties of the tensor of inertia. The angular momentum and the tensor of inertia. The equations of motion of the rigid body; the Euler equations. The spherical free top. The symmetric free top. The asymmetric free top. The symmetric heavy top.

10. The relativistic mechanics

The principles of the relativity theory. The Lorentz transformations. Minkowski space-time, the Lorentz and Poincaré groups. The world-line, the proper time, the ideal clock, the four-velocity and the four-acceleration. The lagrangian of a free particle. The relativistic energy and momentum. The lagrangian description of the interaction between particles and fields. The interaction with a scalar field. A charged particle interacting with the electromagnetic field.

11. The canonical formulation of mechanics

The purpose of the canonical formulation. The Legendre transformation. The canonical equations of Hamilton. Examples of hamiltonians. The Poisson brackets.; their definition, algebraic properties, the Jacobi-Poisson theorem about first integrals. Examples of calculation of the Poisson brackets. The variational principle for the Hamilton equations. The fundamental integral invariant of mechanics. The Jacobi variational principle. The universal integral invariant of Poincaré. The Lee Hwa Chung theorem. Higher integral invariants, the Liouville theorem. The Poincaré theorem about return. The canonical transformations. The Hamilton-Jacobi equation.

12. The elements of continuum media mechanics

The notion of continuum media. The local and substantial derivatives. The continuity equation. The dynamical principles of Cauchy. The Cauchy theorem about existence of the stress tensor. The material equations. The Euler fluid. The Navier-Stokes equation.

1. W. Rubinowicz, W. Królikowski: Mechanika teoretyczna.
2. G. Białkowski: Mechanika klasyczna.

Physics I, II, III, Mathematics.

Pass of class exercises on the basis of solving problems at home and colloquia, written and oral exams.

Course: 210 Electronics, electronic laboratory

Lecturer: dr hab. Tadeusz Stacewicz

Semester: winter

3 every two weeks

3 every two weeks

Code: 06.503210

Credits: 4

Digital integrated cirquits. Application of computers in experiments. Analog integrated circuits (amplifiers, stabilisators). Noise.

During practical laboratory work students use computer-controlled measurement setups. Students learn about standard measurement devices and electronic measurement techniques (signal-to-noise ratio enhancement, selective detection, phase detection, one- and multichanel signal analysis, methods of nuclear electronics, photon counting). Comparison of theory and experiment is discussed.

1. H. Abramowicz, Jak analizować wyniki pomiarów?
2. G. L. Squires, Praktyczna fizyka.
3. U. Tietze, Ch. Schenk, Układy półprzewodnikowe.
4. P. Horovitz, Sztuka elektroniki.
5. T. Stacewicz, A. Kotlicki, Elektronika w laboratorium naukowym.

Introductory laboratory, Physics I and II, Mathematics I and II.

Pass of laboratory exercises, written and oral examination.

Course: 211 Computer programming II

Lecturer:

Semester: winter

Lecture hours per week: 0

Class hours per week: 4

Code: 11.002211

Credits: 5

1. Advanced programming in C++ (classes and objects, stacks, queues, lists, trees, inheritance, polymorphism).
2. Elements of computer graphics.
3. Software for the hardware (e. g. a mouse or a keyboard).
4. More complex algorithms (numerical analysis, searching, sorting).
5. Elements of programming in FORTRAN.
6. Utilisation of different libraries and procedures.

1. J. Grębosz, Symfonia C++. Programowanie w języku C++ orientowane obiektowo.
2. N. Wirth, Algorytmy + struktury danych = Programy.
3. B. Stroustrup, Projektowanie i rozwój języka C++.
4. A. Sapek, W głąb języka C.
5. P. Klimczewski, lecture notes.

Computer programming I.

Pass of class exercises.

Course: 212 Physical experiments under extreme conditions

Lecturer: prof. dr hab. Marian Grynberg

Semester: winter

Lecture hours per week: 2

Class hours per week: 0

Code: 13.201212

Credits: 2,5

1. Low temperatures. Cooling to low temperatures. Temperature detection in low temperatures. Physical phenomena typical at low temperatures.
2. High magnetic fields. Field sources and field detection. Core magnets, superconducting magnets, Bitter and hybrid magnets. Pulse fields. Physical limitations.
3. High vacuum. Pumps. Physical phenomena used in pressure gauges.
4. Methods of submicron solid state layers production. Thickness monitoring. Physical phenomena in 2D semiconductor structures.
5. High pressure in manostates and diamond anvil cells, manometers.
6. Far infrared spectroscopy. Sources, detection (Golay cell, bolometer), monochromatisation. Differential spectroscopy.
7. Synchrotron radiation: sources, characteristics, and application to condensed matter studies.

Literature:

There is no single handbook.

Physics I and II, Mathematics.

Test examination

Course: 213 Physics V- Experimental thermodynamics

Lecturer: prof. dr hab. Maria Kamińska

Semester: summer

Lecture hours per week: 2

Class hours per week: 2

Code: 13.204213

Credits: 5

1. Description of thermodynamic system
2. Empirical temperature and properties of matter dependent on temperature. International Scale of Temperature.
1. volume thermal expansion
2. electrical thermometers
3. pyrometers
4. liquid crystal displays
5. gas thermometers
3. Clapeyron’s equation for ideal gas and equations for real gases. p-V-T surfaces for real substances.
4. First law of thermodynamics. Concept of internal energy, work and heat in thermodynamics. Transport of heat.
5. Molar heat capacity for ideal gas, real gases, liquids and solids. Heat of phase transitions.
6. Heat engine. Carnot cycle. Heat pump.
7. Entropy. Quasistatical, reversible and non-reversible processes.
8. Second law of thermodynamics. Thermodynamic temperature.
9. Transport phenomena (electrical conduction, heat conduction, diffusion, viscosity). Low temperatures. Joule – Thomson effect. Gas liquefier.

1. J. Ginter, Fizyka IV dla NKF.
2. S. Dymus, Termodynamika.
3. A. K. Wróblewski, J. A. Zakrzewski, Wstęp do fizyki, tom 2.
4. J. Orear, Fizyka, tom 1.
5. W. Sears, G. L. Salinger, Thermodynamics, Kinetic Theory and Statistical Thermodynamics.

Prerequisites:

Pass of class exercises, written and oral examination.

Course: 301B Quantum mechanics I

Lecturer: dr hab. Marek Olechowski

Semester: winter

Lecture hours per week: 4

Class hours per week: 4

Code: 13.205301B

Credits: 10

1. Basic definitions in quantum mechanics.
2. Schrödinger equation.
3. Bound states.
4. Collision theory.
5. Symmetries in quantum mechanics.
6. Spin.
7. Perturbation calculus.
8. Radiation.
9. Relativistic wave equation.

1. L. Schiff, Mechanika kwantowa.
2. L. Landau, E. Lifszyc, Mechanika kwantowa.

Mathematical analysis I-III (B or C), Algebra (B or C).

Physics I-IV, Classical mechanics or Modern theoretical mechanics.

Written and oral examination.

Course: 302A Introduction to nuclear and elementary particle physics

Lecturer: prof. dr hab. Jan Żylicz

Semester: winter

Lecture hours per week: 2

Class hours per week: 1

Code: 13.505302A

Credits: 4

1. First contact with the subatomic physics
2. Experimental methods of subatomic physics
3. The force between nucleons. The deuteron
4. Nuclear models
5. Spontaneous transformations and excited states of nuclei
6. Nuclear reactions in laboratory and stellar environments
7. Nuclear physics and society
8. Physics of hadrons
9. Elementary particles
10. Symmetries and conservation laws
11. Perspectives of the subatomic physics

1. E.Skrzypczak, Z.Szefliński, Wstęp do fizyki jądra atomowego i fizyki cząstek elementarnych.
2. I. Strzałkowski, Wstęp do fizyki jądra atomowego.
3. T.Mayer-Kuckuk, Fizyka jądrowa.
4. D.H.Perkins, Introduction to high-energy physics
5. R.J.Blin-Stoyle, Nuclear and particle physics

For further reading:

6. K.S.Krane, Introductory nuclear physics
7. H.Frauenfelder, E.M.Henley, Subatomic physics

Physics I, II, III, IV.

• two colloquia of solving problems (middle and end of the semester);
• - oral examination.

Course: 302B Introduction to quantum theory of atomic nuclei

Lecturer: prof. dr hab. Stanisław G. Rohoziński

Semester: summer

Lecture hours per week: 2

Class hours per week: 2

Code: 13.506302B

Credits: 5

The lecture is an elementary (based on the quantum mechanics I) introduction to the theory of nuclear structure. On the one hand it is a continuation of the quantum mechanics I applied to nuclear systems. On the other hand it deals with an introductory description of quantum states of nucleons in nuclei and construction of quantum nuclear models.

Components of atomic nuclei: protons and neutrons. Isotopic spin. Nuclear forces and their symmetries. Nuclear two-body problem – deuteron. Collisions of nucleons. Determination of nuclear forces – the inverse problem in quantum mechanics. Nuclear three-body problem – tryton, three-body forces. Nuclear mean-field potential. A nucleon in mean-field. Shell model and the Nilsson model. Nuclear deformation. A nucleon weakly bounded – limits of nuclear stability. Classical nuclear models: the liquid drop model, the rigid body model. The quantization of classical models. The collective model of the nucleus.

1. G. Györgyi, Zarys teorii jądra atomowego.

2. J.M. Eisenberg, W. Greiner, Nuclear Models.

3. S.G. Nilsson, I. Ragnarsson, Shapes and Shells in Nuclear Structure.

Suggested: Physics IV, Classical mechanics, Mechanics of continuous media,

Introduction to the nuclear and elementary particle physics

Required: Quantum mechanics I

Pass of class exercises, written and oral examination.

Course: 303A Physics laboratory II (a)

Head: prof. dr hab. Czesław Radzewicz

Semester: winter or summer

Lecture hours per week: -

Class hours per week: 11

Code: 13.205303

Credits: 13,5

The main purpose of this laboratory is to teach students the experimental techniques used in different areas of physics. There are approx. 40 different exercises divided into five groups: solid state physics, optics, nuclear physics, elementary particle physics, crystal structure. Students can freely select an exercise from a given group but each next exercise has to be from another group. It takes typically from 3 weeks to complete the experimental part of a given exercise. Students work individually and are supervised by assistants. Each exercise contains the following parts: literature study, entrance examination, experiment, data evaluation and preparation of a written report, final discussion. The report has to be written in a form of short scientific publication. Each exercise is graded by the supervising assistant.

The laboratory is divided into two parts: part a (3 exercises), part b (2 exercises). The division is formal and meant only so the student can get different number of credit points.

A list of textbooks (journal papers) is provided for each exercise.

Full Physics laboratory I.

Final grade is an average of the grades from the exercises completed.

Course: 304A Numerical methods A I

Lecturer: prof. dr hab. Ernest Bartnik

Semester: winter

Lecture hours per week: 2

Class hours per week: 3

Code: 11.003304A

Credits: 6

Lecture for students familiar with C language.

1. Introduction: conventions and standards.
2. Interpolation, extrapolation, spline.
3. Integration.
4. Random number generators.
5. Equation solving.
6. Minimalisation.
7. Linear algebra.

W. H. Press, Numerical Recipes in C.

Programming in C.

Pass of class exercises, examination.

Course: 304B Numerical methods B I

Lecturer: dr Maciej Pindor

Semester: winter

Lecture hours per week: 2

Class hours per week: 2

Code: 11.003304B

Credits: 5

A comprehensive review of methods used in numerical analysis to solve a wide class of numerical problems is presented. The problems discussed are: systems linear and nonlinear equations (roots of polynomials included), eigenproblem, interpolation and approximation (polynomials, radial functions, Pade Approximants), numerical integration, numerical Fourier analysis (FFT)

The aim of the lecture is to present a practical application of the methods though an analysis of a computational complexity, or stability and precision of some methods is also discussed.

1. A. Ralston, Wstęp do analizy numerycznej.
2. J. Stoer, R. Bulirsh, Introduction to Numerical Analysis.
3. W. H. Press et al., Numerical Recipes.
4. J.D. Lambert, Numerical Methods for Ordinary Differential Systems.
5. D. Potter, Metody obliczeniowe fizyki.

Mathematical analysis.

Pass of class exercises, written and oral examination.

Course: 305 Electrodynamics of continuous media

Lecturer: prof. dr hab. Jan Blinowski

Semester: summer

Lecture hours per week: 3

Class hours per week: 3

Code: 13.206305A

Credits: 7,5

1. Electrostatics in vacuum.
2. Electrostatics and thermodynamics of dielectrics.
3. Steady currents.
4. Magnetostatics, thermodynamics of magnetic media.
5. Time dependent fields and currents. Maxwell equations and conservation laws.
6. Propagation of electromagnetic waves.
7. Radiation.

1. J. D. Jackson Elektrodynamika klasyczna.
2. L. Landau, E. Lifszyc Elektrodynamika ośrodków ciągłych.

Suggested: Classical mechanics.

Pass of class exercises, written and oral examination.

Course: 305B Electrodynamics and elements of field theory

Lecturer: prof. dr hab. Józef Namysłowski

Semester: summer

Lecture hours per week: 3

Class hours per week: 3

Code: 13.206305B

Credits: 7,5

1. Electrostatics,
2. Boundary-Value Problems,
3. Complete Set of Functions,
4. Dielectrics,
5. Magnetostatics,
6. Time-Varying Electrodynamics,
7. Special Theory of Relativity,
8. Dynamics of Charged Particles, and of Electromagnetic Field
9. Special Anti-Theory of Relativity (an example of total misunderstanding of Special Relativity by the representative of New Age, Fritjof Capra).

1. J. D. Jackson, Classical Electrodynamics, John Wiley and Sons, Inc., New York, London, Sydney, Toronto, Second Edition 1975,
2. L. D. Landau and E. M. Lifszyc, Field Theory, Second Edition.

Mathematical methods of physics, Quantum mechanics I, Classical mechanics.

Pass of class exercises, two colloquia, written and oral examination.

Course: 306 Introduction to optics and solid state physics

Lecturer: dr hab. Andrzej Witowski and dr hab. Tadeusz Stacewicz

Semester: summer

Lecture hours per week: 3

Class hours per week: 3

Code: 13.206306

Credits: 7,5

1. Interaction of electromagnetic radiation with matter - microscopic picture (Einstein’s coefficients “semiclassical” and quantum description), macroscopic description with dielectric function, relation to measurable quantities (transmission and reflectivity). Emission of light - shape of spectroscopic line, homogenous and nonhomogenous broadening. Quantum light amplification and generation (LASER).
2. Atomic hydrogen and alkali metals states. Effect of perturbation on energy levels of atoms - Stark effect, Kerr effect, Zeeman effect and Faraday effect. Description of atoms including electronic spin - spinors.
3. Description of multi electron atoms – exchange interaction, Hartree, Hartree-Fock and central field approximation, spin-orbit interaction, LS and jj coupling - spectroscopic levels.
4. Rydberg atoms.
5. Molecules - adiabatic (Born-Oppenheimer) approximation, electronic states (bonds), motion of nuclei (rotations and oscillations). Symmetry and its effect on properties of - degeneration - interaction with EM radiation.
6. Periodic structures – Bravais lattices, base, elementary cell, symmetry of periodic structures.
7. Interaction with X-rays – diffraction on atomic and molecular gas, diffraction on periodic structures (Laue conditions, inverse lattice and Brillouin zones).
8. Liquid and quasi-crystals - their properties and description.
9. Crystals - bonds in crystals, bad structure (Bloch function and theorem), band structure investigation, free carriers and conductivity (Drude model), doping, lattice vibrations (Debye model).

1. J. Ginter Wstęp do fizyki atomu, cząsteczki i ciała stałego, PWN.
2. Gołębiewski Elementy mechaniki i chemii kwantowej, PWN.
3. W. Kołos Chemia kwantowa, PWN.
4. A. Kopystyńska Wykłady z fizyki atomu, PWN.
5. Ch. Kittel Wstęp do fizyki ciała stałego, PWN.

Introductory Physics course (I-V), Algebra, Analysis, Mathematical methods of physics, Quantum physics (mechanics).

Pass of class exercises, written and oral examinations.

Course: 307B Physics laboratory II (b)

Head: prof. dr hab. Czesław Radzewicz

Semester: winter or summer

Lecture hours per week: -

Class hours per week: 7

Code: 13.205307

Credits: 8,5

The main purpose of this laboratory is to teach students the experimental techniques used in different areas of physics. There are approx. 40 different exercises divided into five groups: solid state physics, optics, nuclear physics, elementary particle physics, crystal structure. Students can freely select an exercise from a given group but each next exercise has to be from another group. It takes typically from 3 weeks to complete the experimental part of a given exercise. Students work individually and are supervised by assistants. Each exercise contains the following parts:

literature study, entrance examination, experiment, data evaluation and preparation of a written report, final discussion. The report has to be written in a form of short scientific publication. Each exercise is graded by the supervising assistant The laboratory is divided into two parts: part a (3 exercises), part b (2 exercises). The division is formal and meant only so the student can get different number of credit points.

A list of textbooks (journal papers) is provided for each exercise.

Full Physics laboratory I.

Final grade is an average of the grades from the exercises completed.

Course: 308 Fundamentals of X-ray and neutron diffraction

Lecturer: prof. dr hab. Jerzy Gronkowski

Semester: winter

Lecture hours per week: 2

Class hours per week: 0

Code: 13.205308

Credits: 2,5

1. Basic knowledge of X-rays (X-ray tube, characteristic and continuous spectrum; synchrotron sources, synchrotron radiation characteristics, insertion devices: wigglers and undulators; interactions of X-rays with matter: real absorption, inelastic (Compton) scattering, elastic (Thomson and Rayleigh) scattering by free electrons, Rayleigh scattering by atoms; X-ray refraction, total external reflection, X-ray reflectometry).
2. Basic knowledge of neutrons (neutron as a particle; neutron sources: reactors and spallation sources, neutron spectra, de Broglie waves of neutrons of different energies, thermal neutrons; neutron scattering by atoms: cross section, scattering length and its dependence on atomic number, isotopic inconsistency; neutron refraction).
3. Elements of crystallography (point lattice, translation symmetry, crystallographic systems, crystal symmetry, Bravais lattices, examples of crystal structures, reciprocal lattice, Brillouin zones, Wigner-Seitz cell).
4. X-ray diffraction (Laue conditions, Bragg condition, diffraction in reciprocal lattice; kinematic theory, intensities of reflected beams, structure factor, Laue and Bragg geometry; X-ray topography and other experimental methods).
5. Neutron diffraction (structure factors for neutrons, comparison with X-rays).
6. Experimental methods of X-ray and neutron diffraction (Laue method, rotating-crystal method, Debye-Scherrer method, diffractometry, crystal structure determination).

1. J. Gronkowski, Materiały do wykładu 1996/97 (biblioteka IFD UW)
2. Z. Trzaska Durski, H. Trzaska Durska, Podstawy krystalografii strukturalnej i rentgenowskiej.
3. Z. Bojarski, E. Łągiewka, Rentgenowska analiza strukturalna.
4. N. W. Ashcroft, N. D. Mermin, Fizyka ciała stałego.

Suggested: Introduction to atomic, molecular and solid state physics or Introduction to optics and solid state physics (since 1998/99), Electrodynamics of continuous media.

Required: Physics I, II, III, IV.

Examination.

Course: 309A Topics in elementary particle physics

Lecturer: prof. dr hab. Barbara Badełek

Semester: summer

Lecture hours per week: 2

Class hours per week: 0

Code: 13.506309A

Credits: 2,5

The programme varies from year to year to account for the latest results and their interpretations.

It encompasses:

1. Basic ideas, classification and review of interactions.

2. Experimental methods: accelerators, beams, targets, detectors, research centres.

3. Elastic, inelastic and deep inelastic scattering of leptons on atomic nuclei and nucleons, quark-parton model, quantum chromodynamics.

4. Standard Model, (grand) unification of interactions.

5. Physics of neutrinos: cosmic, atmospheric and accelerator-made.

6. Contemporary Universe, Big Bang Model, inflation.

The course is based on latest communications of scientific results. Therefore lecture notes are the basic reading. Copies of selected plots and diagrams are also distributed.

1. B. R. Martin and G.Shaw, “Particle Physics”, 2-nd edition, J. Wiley & Sons, 1997

2. D. H. Perkins, “Introduction to High Energy Physics”, 3-rd edition, Addison-Wesley, 1989

3. C. Sutton, “Spaceship neutrino”, Cambridge University Press, 1992

4. F. E. Close, “Cosmic onion”, Heinemann Educational Books, 1983

Introduction to nuclear and particle physics.

Written test.

Course: 309B Introduction to elementary particle physics

Lecturer: dr hab. Marek Olechowski

Semester: summer

Lecture hours per week: 2

Class hours per week: 0

Code: 13.506309B

Credits: 2,5

Syllabus:

1. F.E. Close, Kosmiczna Cebula.
2. F.E. Close, An introduction to quarks and partons.
3. E.W. Kolb, M.S. Turner, The early Universe.

Physics IV, Quantum mechanics I

Written examination.

Course: 310 Introduction to geophysics

Lecturer: prof. dr hab. Marek Grad

Semester: summer

Lecture hours per week: 2

Class hours per week: 0

Code: 13.204310

Credits: 2,5

1. Planetology

Classification of bodies in Solar System; collisional effects in Solar System.

2. Figure of the Earth

The shape of the Earth; size of the Earth; rotary ellipsoid; gravitational field; geoid; isostasy.

3. Seismology

Spatial distribution of earthquakes; seismometry; magnitude and energy of the earthquake; Mercalli and Richter scales; P and S body waves; surface waves; Jeffreys-Bullen travel time; seismic waves in the Earth; Earth structure.

4. Magnetism of the Earth

Magnetic field of the Earth; declination and inclination; drift of the magnetic field; magnetic poles; reverse of the polarity; linear magnetic anomalies; paleomagnetism.

5. Continental drift

Lithospheric plates; trenches and ridges; heat flow of the Earth; elasticity of the Earth; convection in the Earth interior; plate motion and tectonic reconstruction.

6. Atmosphere of the Earth

Structure of the atmosphere; global system of winds on the Earth; origin of clouds and falls – microphysical processes; properties of radiation in atmosphere; greenhouse effect; ozone layer.

1. L. Czechowski, Tektonika płyt i konwekcja w płaszczu Ziemi.
2. E. Stenz, M. Mackiewicz, Geofizyka ogólna.
3. S. P. Clark, Budowa Ziemi.
4. R. M. Goody, J. C. G. Walker, O atmosferach.

Prerequisites:

Oral examination.

Course: 311 Introduction to biophysics

Lecturer: prof. dr hab. Bohdan Lesyng

Semester: summer

Lecture hours per week: 2

Class hours per week: 0

Code: 13.906311

Credits: 2,5

Syllabus:

1. W. Kołos, Chemia kwantowa.
2. M. Fikus, Inżynierowie żywych komórek.
3. M. Fikus, Biotechnologia .

Supplementary literature:

1. P. S. Agutter et al., Energy in Biological Systems.
2. Ch. Cantor, P. R. Schimmel, Biophysical Chemistry.
3. L. A. Blumenfeld, Problemy fizyki biologicznej.
4. Biologia molekularna. Informacja genetyczna, red. Z.Lassota.
5. L. Stryer, Biochemistry.
6. W. Saenger, Nucleic Acids Structure.

Physics I, II, III, IV.

Examination.

Course: 312A Numerical methods A II

Lecturer: prof. dr hab. Ernest Bartnik

Semester: summer

Lecture hours per week: 2

Class hours per week: 3

Code: 11.004312A

Credits: 6

Methods for finding numerical solutions of ordinary and partial differential equations are discussed.

For ordinary equations one-step methods with constant and variable step are presented, as well as multi-step methods.

Boundary values problem is solved using multi-shooting method, but band matrix method is also mentioned.

For partial differential equations both, boundary values problems (overrelaxation method), as well as initial values (with different schemes of the first and second order in time) are presented. As the first part of the lecture, one aim at practical applications of the methods discussed, but some analysis of the stability and precision is also used.

W. H. Press, Numerical Recipes in C.

Programming in C.

Pass of class exercises, examination.

Course: 312B Numerical methods B II

Lecturer: dr Maciej Pindor

Semester: summer

Lecture hours per week: 2

Class hours per week: 2

Code: 11.004312B

Credits: 5

Syllabus:

1. A. Ralston, Wstęp do analizy numerycznej.
2. J. Stoer, R. Bulirsh, Introduction to Numerical Analysis.
3. W. H. Press i in., Numerical Recipes.
4. J.D. Lambert, Numerical Methods for Ordinary Differential Systems.
5. D. Potter, Metody obliczeniowe fizyki.

Mathematical analysis.

Pass of class exercises, written and oral examination.

Course: 313 Mechanics of continuous media

Lecturer: prof. dr hab. Jarosław Piasecki

Semester: winter

Lecture hours per week: 3

Class hours per week: 2

Code: 13.205313

Credits: 6,5

1. Introduction:

the notion of continuum, the object of continuum mechanics.

2. Tensors and elementary differential geometry.
3. Kinematics of a continuum:

Description of the motion (the Lagrange and the Euler pictures),

Description of deformations.

4. Dynamics of a continuum:

Stress tensor, equations of motion, conservation laws.

5. Hydrodynamics of an ideal fluid:

Euler’s equation of motion, hydrostatics, Bernoulli equation, waves.

6. Hydrodynamics of a viscous fluid:

Navier-Stokes equation, energy balance (phenomenon of dissipation), sound waves, incompressible flows, Reynold’s number, turbulence.

7. Linear elasticity theory of solids:

Linear approximation, equations of the theory of elasticity, examples of static and dynamic problems.

L.Landau, E.Lifszic, Hydrodynamika oraz Teoria sprężystości.

Classical mechanics.

Pass of class exercises and examination.

Course: 314 Physics of relativistic nuclei collisions

Lecturer: prof. dr hab. Ewa Skrzypczak

Semester: summer

Lecture hours per week: 2

Class hours per week: 0

Code: 13.506314

Credits: 2,5

1. Basics of fundamental interactions and partons.
2. Experimental tools (accelerators and detectors).
3. Computer simulations as an indispensable part of experiment and data interpretation.
4. What is measured: global characteristics, characteristics of different particles production. Determination of temperature, density and size of emitting sources. Correlations. Individual events analysis.
5. Theoretical models and their predictions (including quark-gluon plasma expected by QCD).
6. Summary of the today state of the art.
7. Planned experiments (end of XX and beginning of XXI century).

Lecture notes, review papers.

Introduction to nuclear and particle physics.

Oral examination.

Course: 315 Physical methods of environmental studies (for students of physics and MSOŚ)

Lecturer: many lecturers (coordination prof. dr hab. A. Kopystyńska)

Semester: winter and summer

Lecture hours per week: 2

Class hours per week: 0

Code: 13.205315

Credits: 5

dr Piotr Jaracz - Radioactivity in human environment – a compendium of physics of radioactivity and radioactive pollution. Statistic in radiometry and dosimetry (basic notions, regulations). Detection of ionising radiation: physics and technology. Comprehension of radiation risk: history, psychometric approach to radiation risk. - 10 h

dr hab. Wojciech Gadomski - Lidar – interaction of electromagnetic radiation with matter; optical detection of air pollution; lasers and detectors; measurement systems (various kinds of lidar) - 10 h

prof. dr hab. Tomasz Szoplik - Remote sensing and satellite image processing – definition and tasks. Spatial, intensity and spectral information. Black body radiation. Solar spectrum. Absorption spectra. Resolution of imaging systems. Synthetic aperture optics. Convolution and local convolution. Digital and optical methods of convolving. Rank order filters. Morphological filters. Histogram and its modification. Noise removal and detail enhancement. Unsupervised and supervised classification. - 8 h

Summer semester:

dr Bogumiła Mysłek-Laurikainen - Radioecology – natural radioactivity and radioactive pollution in environment; monitoring of radioactive contamination; nuclear power stations – contribution to world energy consumption; radioactive waste policy; nuclear weapons tests; radioecology in future - 10 h

dr Ryszard Balcer - Physics of atmosphere – definitions of ecology, ecosystem and monitoring; geospheres; solar and terrestrial radiation; energy balance of Earth; instrumentation for solar radiation measurements, micrometeorological measurements; aerosols in atmosphere; clouds chemistry - 10 h

prof. dr hab. Ryszard Stolarski and dr hab. Zygmunt Kazimierczuk - Pollution of environment and protection mechanisms – organic pollution of water and soil; enzymatic decomposition of some mutagenic and cancerogenic agents; molecular foundations of heredity; molecular mechanisms of genetic reparation of damages caused by environmental pollution - 10 h.

Lecture notes available in the library of IFD.

Prerequisites:

Test examination.

Course: 316A Seminar on modern physics

Lecturer: prof. dr hab. Andrzej Twardowski

Semester: winter

Hours per week: 2

Code: 13.205316A

Credits: 2,5

Syllabus:

The aim of the seminar is to present basic problems of the modern experimental and theoretical physics, with focus on the research currently in progress at Warsaw University. The seminar is designed as a series of 26 one-hour lectures given by scientists from different research groups. After the presentations students should recognise the activity at Faculty of Physics and the relation of this activity to the worldwide research. This way the seminar should help the students of the third year to make the decision concerning their specialisation in physics.

Literature:

Prerequisites:

Pass for students who attend seminars.

Course: 316B Seminar on theoretical physics

Lecturer: prof. dr hab. Stefan Pokorski and dr hab. Piotr Chankowski

Semester: winter and summer

Hours per week: 2

Code: 13.205316B

Credits: 2,5

The aim of the seminar is to help students in selection of theoretical physics specialisation. Contemporary theoretical research fields are presented with a special emphasise of research in the Physics Faculty of WU.

Literature:

Prerequisites:

Pass for students who attend seminars.

Course: 317 Microscopy, microdiffraction and microanalysis.

Lecturer: dr Jacek Jasiński

Semester: winter

Lecture hours per week: 2

Class hours per week: 0

Code: 13.205317

Credits: 2,5

The aim of the lecture is to introduce experimental methods of analytical electron microscopy.

Syllabus:

1. Introduction – relationships between microscopy, diffraction and spectroscopy. Transmission electron microscope as a universal tool for micro- and nano-scale materials studies.

2. Electron sources. Electron lens and their aberrations. Magnification and resolution. Electron detection and display. Different types of electron microscopes - TEM, SEM, STEM.

3. Interaction of electrons with matter. Elastic and inelastic scattering. Scattering with phonons and plasmons. Auger electrons. Characteristic X-rays emission.

4. Diffraction contrast - principles and applications. Investigations of defects in crystalline materials.

5. Electron diffraction. Atomic scattering amplitude. Scattering from a crystal - concept of "reciprocal lattice".

6. Different types of electron diffraction - SAED, CBDE, LACBED, RHEED.

7. Electron diffraction - applications.

8. High-resolution electron microscopy (HREM) - principles, applications and limitations.

9. Electron microscopic "in situ" experiments.

10. Energy-dispersive x-ray spectroscopy - detection and analysis, spatial resolution and minimum detectability.

11. Electron energy-loss spectroscopy- comparison of EELS and EDS, applications of EELS.

12. TEM specimen preparation - preparation methods for crystals and biological materials, limitations and disadvantages of specimen preparation.

Literature:

Prerequisites:

Oral examination.

Course: 322 Introduction to classical and quantum field theory

Lecturer: prof. dr hab. Krzysztof Meissner

Semester: summer

Lecture hours per week: 2

Class hours per week: 1

Code: 13.206322

Credits: 6,5

Classical fields, symmetries, conservation principles, scalar and spinor fields, symmetry braking, Higgs mechanism, field quantisation, trajectory integrals, S matrix.

The lecture (together with Modern methods of quantum field theory, course number 455) introduces to the methods of quantum field theories. The final goal is to introduce QED, QCD and electroweak theory as theories of high energy elementary processes. The lecture also founds a theoretical basis for phenomenological lecture.

1. S. Pokorski, Gauge Field Theories.
2. J. Bjorken, S. Drell, vol. 1: Relativistic Quantum Mechanics, vol. 2: Relativistic Quantum Fields.
3. C. Itzykson, J. B. Zuber, Quantum Field Theory.

Quantum mechanics I, Classical electrodynamics

Pass of class exercises. Oral and written examinations.

Course: 333 Quantum mechanics 3/2

Lecturer: prof. dr hab. Krzysztof Wódkiewicz

Semester: summer

Lecture hours per week: 3

Class hours per week: 0

Code: 13.206333

Credits: 4

1. The phase space.

Phase space in quantum mechanics. Coherent states and the phase space. The Wigner function and other quasi-distribution functions in phase space. Generalised quasi-distribution functions in phase space for arbitrary operator orderings. Feynman path integral in phase space. Phase space for spin. Spin coherent states. Feynman path integral in phase space.

2. Bell inequalities and hidden parameters.

Local realities in quantum correlations. Einstein Podolsky Rosen (EPR) correlations. Einstein ghostfield. Entangled states. variables and the EPR correlations. Hidden variables and Bell inequalities. Quantum Malus law. Classical limit of EPR correlations. Quantum ghost-fields in the EPR correlations. Reality and nonlocality on photon correlations. Greenberger Horne and Zeilinger (GHZ) correlations. Entropic Bell inequalities.

3. Quantum measurement theory.

Operational approach to quantum measurements. Operational approach to quantum theory of measurement. Quantum propensity and algebras of operational observables. Quantum filters and entanglement during measurements. Operational measurements of Q and P. Operational uncertainty relations. Operational measurement of the quantum phase. Quantum trigonometry. Quantum decoherence. Zeno measurements. Quantum jumps.

Selected original papers.

Quantum mechanics I, Electrodynamics.

Oral examination.

Course: 401 Statistical physics I

Lecturer: prof. dr hab. Marek Napiórkowski

Semester: winter

Lecture hours per week: 3

Class hours per week: 3

Code: 13.207401

Credits: 7,5

1. Introduction to probability theory.
2. Classical and relativistic dynamics in phase space.
3. Classical and quantum probability distributions in phase space.
4. Equilibrium statistical ensambles. Entropy.
5. Applications of statistical ensambles.
6. Bose and Fermi gases.
7. Theory of real gases.
8. Elements of phase transitions.
9. Dynamical approaching of equilibrium states.
10. Elements of fluctuation theory.

1. L. Landau, L. Lifszyc, Fizyka Statystyczna.
2. K. Huang, Fizyka Statystyczna.

Quantum mechanics I, electrodynamics.

Pass of class exercises. Oral and written examination.

Course: 402 Thermodynamics

Lecturer: dr Krzysztof Rejmer

Semester: summer

Lecture hours per week: 2

Class hours per week: 2

Code: 13.206402

Credits: 5

Syllabus:

Literature:

Prerequisites:

Pass of class exercises. Oral and written examination.

Course: 501 Astrophysics for physicists

Lecturer: prof. dr hab. Michał Jaroszyński

Semester: summer

Lecture hours per week: 2

Class hours per week: 0

Code: 13.704501

Credits: 2,5

1. The Universe: structure; Newtonian model; standard model; cosmic background radiation; primordial nucleosynthesis; the emergence of structure; gravitational lensing.
2. Galaxies: morphology; dark matter; active galactic nuclei; radiogalaxies; quasars.
3. The Milky Way: kinematics; stellar populations; spiral arms.
4. Stars: models; evolution; end products; supernovae; solar neutrino problem; neutron stars and pulsars; black holes.
5. Planetary systems.

1. S. Weinberg, Pierwsze 3 minuty
2. M. Jaroszyński, Galaktyki i Wszechświat.
3. M. Kubiak, Gwiazdy i materia międzygwiazdowa.

Suggested: Introduction to nuclear and particle physics.

Required: Physics I and II; Mathematical Analysis I and II, Algebra.

Examination.

Course: A201 Numerical methods (for students of astronomy)

Lecturer: dr Michał Szymański

Semester: winter

Lecture hours per week: 2

Class hours per week: 2

Code: 11.003A201

Credits: 5

1. Numerical algorithms; methods of equation solving.
2. Approximation - least squares method.
3. Interpolation of function and experimental data.
4. I order differential equations. Iteration methods. Runge-Kutta method.
5. Numerical integration and differentiation. Gauss and Newton-Cotes methods.
6. Solving of linear equations sets.
7. Monte Carlo methods.

Classes contain introduction to DOS, UNIX and FORTRAN.

1. Metody numeryczne – dowolny
2. R. Kott , Fortran.
3. K. Walczak, Programowanie w języku Fortran 77.

Prerequisites:

Pass of class exercises, examination.

Course: A202 Numerical laboratory (for students of astronomy)

Semester: summer and winter

Lecture hours per week: 0

Class hours per week: 3

Code: 11.003A202

Credits: 7,5

1. Use of computer in DOS and Unix system.
2. Processing of text file.
3. Writing, compilation and testing C and FORTRAN programs.
4. X- Windows.
5. Network: mail, ftp, telnet, Netscape.
6. Numerical recipes - overview and examples of applications.

1. DOS, Unix
2. Press et al.: Numerical Recipes.

Numerical methods, programming.

Pass of class exercises.

Course: A203 Computer programming (for students of astronomy)

Lecturer: dr Michał Szymański

Semester: winter

Lecture hours per week: 2

Class hours per week: 2

Code: 11.003A203

Credits: 5

1. Programming in FORTRAN.
2. Programming in C.

1. R. Kott, K. Walczak: Programowanie w języku Fortran 77.
2. B.W. Kernighan, D.M. Ritchie: Język ANSI C.

Prerequisites:

Pass of class exercises, examination.

Course: A301 Introduction to observational astrophysics

Lecturer: prof. dr hab. Andrzej Udalski

Semester: winter

Lecture hours per week: 3

Class hours per week: 4

Code: 13.705A301

Credits: 8,5

1. Sources of information about Universe. Electromagnetic spectrum.
2. Telescopes.
3. Radiation receivers.
4. Photometry.
5. Stellar catalogues.
6. Spectroscopy.

M. Kubiak, Gwiazdy i materia międzygwiazdowa.

Physics I, II, III, IV.

Introduction to astronomy.

Pass of class exercises, examination.

Course: A302 Statistics for astronomy

Lecturer: dr Jacek Chołoniewski

Semester: summer

Lecture hours per week: 4

Class hours per week: 4

Code: 13.205A302

Credits: 10

Syllabus:

Literature:

Algebra and analysis / mathematics.

Pass of class exercises, examination.

Course: A303 Selected topics on general astrophysics

Lecturer: prof. dr hab. Marcin Kubiak

Semester: summer

Lecture hours per week: 3

Class hours per week: 2

Code: 13.706A303

Credits: 6,5

1. Radiation field.
2. Atomic gas.
3. Interaction of radiation and matter.
4. Energy transport in stars.
5. Pulsation of stars.

1. D. Mihalas, Stellar Atmospheres.
2. A. Unsoeld, Physik der Sternatmosphaeren.
3. L. Aller, Atoms, Stars and Nebulae.
4. W. Sobolev, Kurs Tieoreticzeskoj Astrofiziki.
5. W. Rubinowicz, Kwantowa Teoria Atomu.
6. M. Kubiak, Gwiazdy i Materia Międzygwiazdowa.

Introduction to atomic, molecular and solid state physics or Introduction to optics and solid state physics, Quantum mechanics I.

Colloquium, examination.