Consider a quantum system with just three linearly independent states. Suppose the Hamilto...

Consider a quantum system with just three linearly independent states. Suppose the Hamiltonian, in matrix form, is

where V0 is a constant, and e is some small number (e 1).

(a) Write down the eigenvectors and eigenvalues of the unperturbed Hamiltonian

= 0).

(b) Solve for the exact eigenvalues of H. Expand each of them as a power series in e, up to second order.

(c) Use first- and second-order nondegenerate perturbation theory to find the approximate eigenvalue for the state that grows out of the nondegenerate eigenvector of H0. Compare the exact result, from (a).