Franz Schwabl Quantum Mechanics 4th Edit · Problem 3.12

The Uncertainty Relation

Physics — Quantum Mechanics · half-harmonic-oscillator

Problem

What are the energy levels and the eigenfunctions for a potential of the form

V(x) = \begin{cases} \infty & x \leq 0 \\ \dfrac{m\omega^2 x^2}{2} & x > 0 \end{cases} \quad?