Introduction to Quantum Mechanics · Problem 3.6

Formalism — David J. Griffiths

Physics — Quantum Mechanics · eigenvalues_eigenfunctions

Problem

Consider the operator Q^=d2/dϕ2\hat{Q} = d^2/d\phi^2, where (as in Example 3.1) ϕ\phi is the azimuthal angle in polar coordinates, and the functions are subject to Equation 3.26. Is Q^\hat{Q} hermitian? Find its eigenfunctions and eigenvalues. What is the spectrum of Q^\hat{Q}? Is the spectrum degenerate?

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