Maslov index for power-law potentials

TL;DR

This paper calculates the Maslov index for one-dimensional power-law potentials in semiclassical quantization, compares it with exact solutions for the inverse square root case, and extends the analysis to spherically symmetric potentials.

Contribution

It provides a new calculation of the Maslov index for power-law potentials and compares it with exact solutions, extending the analysis to spherically symmetric cases.

Findings

Maslov index calculated for inverse square root potential

Comparison with exact solutions confirms the validity

Extension to spherically symmetric potentials included

Abstract

The Maslov index in the semiclassical Bohr-Sommerfeld quantization rule is calculated for one-dimensional power-law potentials. The result for the inverse square root potential is compared with the recently reported exact solution. The case of a spherically symmetric power-law potential is also considered.