Power series Schrodinger eigenfunctions for a particle on the torus

TL;DR

This paper derives eigenvalues and provides a power series representation of eigenfunctions for a particle constrained to move on a torus, advancing analytical methods in quantum mechanics on curved surfaces.

Contribution

It introduces a novel power series approach to explicitly represent Schrodinger eigenfunctions on a torus, which was not previously available.

Findings

Eigenvalues of the particle on a torus are explicitly derived.

A power series representation of the eigenfunctions is established.

The method enhances analytical understanding of quantum states on curved surfaces.

Abstract

The eigenvalues and a series representation of the eigenfunctions of the Schrodinger equation for a particle on the surface of a torus are derived.