To deal with the problem of degenerate states, we will allow an arbitrary linear combination
of those states at zeroth order.
In the following equation, the sum over
is the sum over all the states degenerate with
and the sum over k runs over all the other states.
The full Schrödinger equation is.
By putting both terms together, our calculation gives us the full energy to first order, not just the
It is useful both for degenerate states and for nearly degenerate states.
The result may be simplified to
Jim Branson 2013-04-22