To solve the problem of particles stuck inside an impenetrable shell
of radius , refer to addendum {A.6}.
According to that addendum, the solutions without unacceptable
singularities at the center are of the form
(D.53) |
Because the wave function must be zero at the shell
, must be one of the zero-crossings of
the spherical Bessel functions. Therefore the allowable energy levels
are
(D.54) |
In terms of the count of the energy levels of the harmonic
oscillator, 1 corresponds to energy level
, and each next value of increases the energy
levels by two, so