Given is a hamiltionan H0:
with E1 and E2 being eigenvalues of two eigenstates phi1 and phi2
A distortion W, with W12 = W21* (complex conjugate):
Calculate the eigenvalues and eigenstates of H = H0 + W
See for most info:
it's a two-state perturbation problem
The Attempt at a Solution
I found out most things like how to calculate the eigenvalues. A lot of it is explained at the mentioned site (http://farside.ph.utexas.edu/teaching/qm/lectures/node50.html) The thing I don't get is how they got from the eigenvalues to the eigenstates.
I have tried the following:
( E1 - E1' W12 )(a) (0)
( W21 E2 - E1' )(b) = (0)
with E1' being the first new eigenvalue: E1'=E1 + |W12|^2/(E1-E2)
But I do not get to the answer provided on the site.
I hope I have been clear about my question, so someone can explain it to me. Thanks in advance!