SWKB for the Angular Momentum

Abstract

It has been recently shown [M. Robnik and L. Salasnich, J. Phys. A: Math. Gen.30, 1719 (1997)] that the WKB series for the quantization of angular momentum L converges to the exact value L2=ℏ2l(l+1), if summed over all orders, and gives the Langer formula L2=ℏ2(l+1/2)2 at the leading order. In this work we solve the eigenvalue problem of the angular momentum operator by using the supersymmetric semiclassical quantum mechanics (SWKB), and show that it gives the correct quantization already at the leading order.