For spherically symmetrical potentials we can apply the WKB approximation to the radial part (Equation 4.37). In the case l = 0 it is reasonable to use Equation 9.48 in the form

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 α). Treat only the case l = 0. Show that the spacing between the levels is independent of mass.

Transcribed Image Text:

[TD p(r)dr = (n 1/4) πh, (9.55)