WKB explicit formulae for bound states

Abstract

The radial Schrödinger equation with a central potential is discussed and the pertinent WKB integral is cast in a more convenient form to extract closed formulae for the eigenvalues. These can be deduced in several interesting cases and are of asymptotic nature, i.e. they hold when one of the two quantum numbers appearing in the equation tends to infinity.

Removing degeneration from a WKB explicit formula for bound states

“…Conclusion. -This paper continues a previous work on the same subject [1]. The WKB formulae we present here, within our sufficient assumptions on the potential, discriminate between energy levels, which before were spuriously degenerate.…”

“…l n ref. [ The superposition of a power potential and a Coulomb potential Z/R can be treated as illustrated in [1] (see eqs. ( 4) and ( 11) there): a further correction term will then appear on the r.h.s.…”