The problem is to determine the stationary state wave function
of an atom or ion, in the framework of special relativity and
quantum mechanics, i.e. to find the solution of the eigenvalue
problem;
where H is the Dirac Hamiltonian for an N-electron atom (or ion)
less the rest energy. The state of an atom is specified by its
energy E, as well as with values of the total angular momentum
with eigenvalues
and its projection on an arbitrary but fixed axis (say the Z axis)
with eigenvalues
.
The wave function must obey the Pauli-exclusion principle for
fermions(electrons), i.e., be anti-symmetric with respect to an
interchange of particles.