New approximate radial wave functions for power-law potentials

TL;DR

This paper introduces a new approximation method for radial wave functions in power-law potentials, combining power-law substitution with explicit summation of the leading WKB series to improve accuracy at critical regions.

Contribution

It presents a novel approach that accurately reproduces wave function behavior at key points, enhancing previous approximation techniques for power-law potentials.

Findings

Accurately models wave functions at the origin and turning points

Provides explicit summation of the leading WKB series

Improves approximation accuracy for power-law potentials

Abstract

Radial wave functions for power-law potentials are approximated with the help of power-law substitution and explicit summation of the leading constituent WKB series. Our approach reproduces the correct behavior of the wave functions at the origin, at the turning points and far away from the turning points