A Modern Approach to Quantum Mechanics · Problem 10.9

Time-Independent Perturbations — John S. Townsend

Physics — Quantum Mechanics · one-dimensional-potential-well-bound-state

Problem

Use the techniques illustrated in Section 10.3 to solve the one-dimensional potential well

V(x) = \begin{cases} -V_0 & |x| < a \\ 0 & |x| > a \end{cases}

Show that there always exists at least one bound state for this well.