Introduction to Quantum Mechanics · Problem 7.5

Time-Independent Perturbation Theory — David J. Griffiths

Physics — Quantum Mechanics · second_order_perturbation

Problem

(a) Find the second-order correction to the energies

(E_n^2)

for the potential in Problem 7.1. *Comment:* You can sum the series explicitly, obtaining

-2m(\alpha/\pi\hbar n)^2

for odd

n

. (b) Calculate the second-order correction to the ground state energy

(E_0^2)

for the potential in Problem 7.2. Check that your result is consistent with the exact solution.