Introduction to Quantum Mechanics · Problem 4.11

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · finite_spherical_well

Problem

A particle of mass

m

is placed in a finite spherical well:

V(r) = \begin{cases} -V_0, & r \leq a; \\ 0, & r > a. \end{cases}

Find the ground state, by solving the radial equation with

\ell = 0

. Show that there is no bound state if

V_0 a^2 < \pi^2\hbar^2/8m