Here is an application of the technique developed in Problem 7.34. Consider the Hamiltonian

(a) Find the projection operator P_D (it’s a 3 x 3 matrix) that projects onto he subspace spanned by

Then construct the matrices H̅⁰ and H̅'.
(b) Solve for the eigenstates of H̅⁰ and verify…
i. That its spectrum is nondegenerate,
ii. That the nondegenerate eigenstate of H⁰

is also an eigenstate of H̅⁰ with the same eigenvalue.
(c) What are the “good” states, and what are their energies, to first order in the perturbation?

Transcribed Image Text:

00 a b * - (: : ;) + - ( ; ; ). 0 € 0 00 0 H' = a* 0 C b* c* 0 Hº