Introduction to Quantum Mechanics · Problem 5.27

Identical Particles — David J. Griffiths

Physics — Quantum Mechanics · energy_degeneracy

Problem

Show that most of the energies determined by Equation 5.71 are doubly degenerate. What are the exceptional cases? Hint: Try it for

N = 1, 2, 3, 4, \ldots

, to see how it goes. What are the possible values of

\cos(qa)

in each case?