On the Eigenvectors of the 5D Discrete Fourier Transform Number Operator in Newtonian Basis

Abstract

A simple analytic approach to the evaluation of the eigenvalues and eigenvectors f_n of the 5D discrete number operator is formulated.
This approach is based on the symmetry of the intertwining operators A₅ and  A^T₅ with respect to the discrete reflection operator. A procedure for the
intertwining operators A₅ and  A^T₅ 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 terms of the Newtonian basis polynomials times the lowest eigenvector f₀, as well.