A deformed solution
of Eq. (1) is a superposition of eigenstates of the
angular-momentum operator. The angular-momentum conserving wave function
can be obtained from the state by
applying the angular-momentum projector:

where represents the set of three Euler angles , are the Wigner functions,[15] and is the rotation operator.

The state is no longer a product wave function, but a
complicated superposition of Slater determinants. The operator
is not a projector in the mathematical sense.[1]
It extracts from the intrinsic wave function the component with a projection
along the intrinsic axis of the nucleus. Since is not a good quantum number,
all these components must be mixed, and the mixing coefficients
must be determined by
the minimization of energy. This -mixing is taken into account by assuming
the following form for the eigenstates:

where and denote the Hamiltonian and overlap kernels, respectively.