A Modern Approach to Quantum Mechanics · Problem 10.8

Time-Independent Perturbations — John S. Townsend

Physics — Quantum Mechanics · spherical-potential-well-no-bound-states

Problem

Show that there are no allowed energies

E < -V_0

for the potential well

V = \begin{cases} -V_0 & r < a \\ 0 & r > a \end{cases}

by explicitly solving the Schrödinger equation and attempting to satisfy all the appropriate boundary conditions.