On the eigenvectors of the 5D discrete Fourier transform number operator in Newtonian basis

TL;DR

This paper presents an analytic method for evaluating eigenvalues and eigenvectors of a 5D discrete number operator using symmetry and intertwining operators, establishing a discrete analog of continuous case formulas in the Newtonian basis.

Contribution

It introduces a symmetry-based analytic approach and a sparsealization procedure for discrete operators, creating a new discrete analog of continuous eigenvector formulas.

Findings

Eigenvalues and eigenvectors of the 5D discrete number operator are analytically evaluated.

A sparsealization procedure for intertwining operators is developed.

Discrete analogs of continuous eigenvector formulas are constructed in the Newtonian basis.

Abstract

A simple analytic approach to the evaluation of the eigenvalues and eigenvectors f_n of the 5D discrete number operator N_5 is formulated. This approach is essentially based on the symmetry of the intertwining operators with respect to the discrete reflection operator. A procedure for the sparsealization of the intertwining operators has been developed, which made it possible to establish a discrete analog of the well-known continuous case formula. A discrete analog for the eigenvectors f_n of another continuous case formula is constructed in the Newtonian basis polynomials, times the lowest eigenvector f_0.