Question

Consider an atom in a crystal with two eigenstates ѱ1 and ѱ2 with energies ?1 0...

Consider an atom in a crystal with two eigenstates ѱ1 and ѱ2 with energies ?1
0
, ?2
0
. As the
crystal is compressed, the crystalline field varies and the eigenstates are perturbed. The matrix of the
perturbation in the basis of ѱ1 and ѱ2 is
? = (
0 3?
3? 4?
)

a) What are the first and 2nd order corrections to the energies of the states if ?1
0 ≠ ?2
0
?
b) What are the lowest order correction to the energies if ?1
0 = ?2
0
?

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Answer #1

At the beginning I would like to mention there is some typing problem in the question, hence it was not understood clearly what are the actual things to be found out. However I have shown how to find out the first order energy correction if the perturbing hamiltonian is given in question.

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