Consider a perturbed hydrogen atom whose Hamiltonian, in atomic units, is:
H= -1/2(∆^2) – ½ + b/(r^2) (∆ should be upside down), where b is a
positive constant. The Schrodinger equ. for this hamiltonian can be solved
exactly for the energy eigenvalues. The results for the ground state is:
E = -1/[2(B^2)], where B = [1 + (1 + 8b)^(1/2)]/2.
Use first-order perturbation theory in which the perturbation is b/(r^2) to
compute the ground-state energy of the purturbed system for b=0.01,
b=0.10, b=0.50, b=1.0, and b=10.0.
The Attempt at a Solution
I am not sure how to start this problem. Any hints to get me started?