Removing degeneration from a WKB explicit formula for bound states

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