Perturbation Theory

Suppose we can find the bound states of some Hamiltonian \(H_{0}\) by solving exactly the time-independent Schrödinger equation \(H_{0}\psi _{n}^{(0)}=E_{n}^{(0)}\psi _{n}^{(0)}\) . We calculate the discrete energy levels \(\{ E_{1}^{(0)},E_{2}^{(0)},E_{3}^{(0)},\ldots \}\) and find agreement with the experiment. Invariably then, we wish to see what happens when we perturb the system by what we physically feel is a weak perturbation \(\hat{V}.\)