Point Charge Subject to an Attractive Inverse-Square-Type Potential and Anharmonic-Type Potentials

Abstract

By applying the WKB (Wentzel, Kramers, Brillouin) approximation, we search for bound state solutions to the time-independent Schrödinger equation for an attractive inverse-square potential and anharmonic oscillators that stem from the interaction of a point charge with radial electric fields. We focus on the bound states associated with the s-waves. Further, we obtain the revival time associated with each case studied.

Keywords

• attractive inverse-square potential
• anharmonic oscillators
• WKB approximation
• semiclassical approximation
• quantum revivals