Removing degeneration from a WKB explicit formula for bound statesGiulio Paiano
Dipartimento di Fisica “Michelangelo Merlin”, Università di Bari - via Amendola 173, 70126 Bari, Italy, EU and INFN, Sezione di Bari - Bari, Italy, EU
received 9 September 2009; accepted in final form 23 October 2009; published November 2009
published online 24 November 2009
In this paper we improve a previously established three-dimensional WKB formula of asymptotic nature, which holds when the radial quantum number tends to infinity: a more accurate evaluation of the roots of the WKB integrand yields indeed lower order contributions, which depend on the azimuthal quantum number and remove the degeneration of the energy levels. Improvement of the convergence to the usual WKB eigenvalues is also verified in a number of cases.
03.65.Ge - Solutions of wave equations: bound states.
03.65.Sq - Semiclassical theories and applications.
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