Thermodynamics, Statistical Physics, and Quantum Mechanics

322 SOLUTIONS

of the ground state wave function

where is the Bohr radius.

General

5.70 Spherical Box with Hole (Stony Brook)

In spherical coordinates the eigenfunctions for noninteracting particles of

wave vector are of the form

where and are spherical Bessel functions. The constants A and B
are determined by the boundary conditions. Since we were onlyasked for
the states with we only need and
We can take a linear combination of these functions, which is a particular
choice of the ratio B/A,to make the wave function vanish at

This satisfies the boundary condition at Requiring that thisfunction

vanish at gives