Introduction to Quantum Mechanics · Problem 7.13

Time-Independent Perturbation Theory — David J. Griffiths

Physics — Quantum Mechanics · degenerate_perturbation_theory

Problem

In the text I asserted that the first-order corrections to an

n

-fold degenerate energy are the eigenvalues of the

W

matrix, and I justified this claim as the "natural" generalization of the case

n = 2

. *Prove* it, by reproducing the steps in Section 7.2.1, starting with

\psi^0 = \sum_{j=1}^{n} \alpha_j \psi_j^0

(generalizing Equation 7.17), and ending by showing that the analog to Equation 7.27 can be interpreted as the eigenvalue equation for the matrix

\mathsf{W}