Principles of Quantum Mechanics · Problem 7.3.6

The Harmonic Oscillator — R. Shankar

Physics — Quantum Mechanics · half-harmonic-oscillator

Problem

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Consider a particle in a potential

V(x) = \tfrac{1}{2}m\omega^2 x^2, \quad x > 0

= \infty, \quad x \leq 0

What are the boundary conditions on the wave functions now? Find the eigenvalues and eigenfunctions.