Path integral solution for an angle-dependent anharmonic oscillator

TL;DR

This paper introduces a path integral method to exactly solve a three-dimensional angle-dependent anharmonic oscillator, deriving the energy spectrum and wave functions by separating angular and radial motions.

Contribution

It presents a novel approach using path integrals in spherical coordinates to solve a noncentral anharmonic oscillator exactly, including energy spectra and wave functions.

Findings

Exact calculation of the propagator

Derivation of energy spectrum and wave functions

Separation of angular and radial motions

Abstract

We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we were able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.