Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 7, Problem 7.40P

(a)

To determine

Show that for the two fold degeneracy studied the first order correction to the wave function in degenerate perturbation theory is ψ1=ma,bαVma+βVmbE0Ent0ψn0

(b)

To determine

Show that α and β are determined by finding the eigenvectors of the matric where, [W2]ij=na,bψi0|H|ψm0ψm0|H|ψj0E0Em0 and that the Eigen vectors of this matrix correspond to the second order energies E2.

(c)

To determine

Show that second order degenerate perturbation theory, developed in (b) gives the correct energies to second order for the three state Hamiltonian.

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