For spherically symmetrical potentials we can apply the WKB approximation to the radial pa...

For spherically symmetrical potentials we can apply the WKB approximation to the radial part (Equation 1). In the case l = 0 it is reasonable15 to use Equation 8.47 in the form

 [8.54]

where r0 is the turning point (in effect, we treat r = 0 as an infinite wall) Exploit this formula to estimate the allowed energies of a particle in the logarithmic potential

(for constants V0 and a). Treat only the case l = 0. Show that the spacing between the levels is independent of mass. Partial answer:

Equation 1