The eigenvalues and eigenvectors of the 5D discrete Fourier transform number operator revisited

TL;DR

This paper presents a systematic analytic method for determining the eigenvalues and eigenvectors of the 5D discrete number operator, leveraging the symmetric properties of the 5D discrete Fourier transform.

Contribution

It introduces a novel analytic approach based on symmetry considerations to evaluate eigenvalues and eigenvectors of the 5D discrete number operator.

Findings

Eigenvalues and eigenvectors explicitly derived for the 5D case

Symmetry of the Fourier transform operator is key to the analysis

Method can potentially be extended to higher dimensions

Abstract

A systematic analytic approach to the evaluation of the eigenvalues and eigenvectors of the 5D discrete number operator is formulated. This approach is essentially based on the use of the symmetricity of 5D discrete Fourier transform operator with respect to the discrete reflection operator.