Solution of the Path Integral for the Quantum Pendulum

TL;DR

This paper performs path integral calculations for the quantum pendulum with a cosine potential, demonstrating the resulting Feynman kernel satisfies the Schrödinger equation and providing Green function expressions.

Contribution

It presents an explicit solution of the path integral for the quantum pendulum and derives the Green function, advancing analytical methods in quantum mechanics.

Findings

Feynman kernel satisfies the Schrödinger equation

Explicit Green function expressions are derived

Path integral solution for the cosine potential is obtained

Abstract

Path integration for the potential V={\alpha}cos{\theta} is performed. Satisfaction of the corresponding Schr\"odinger equation by the resulting Feynman kernel is demonstrated. Expressions for the related Green function are presented.