ON A FAMILY OF DISCRETE ND LADDER-TYPE OPERATORS CONSTRUCTED IN TERMS OF THE HERMITIAN TOEPLITZ COMMUTATOR OPERATOR Z_N

Year 2024, Volume: 6 Issue: 2, 24 - 49, 08.11.2024

Miguel Angel Ortiz Natig Atakishiyev

https://doi.org/10.47087/mjm.1467436

Abstract

A development of an algebraic system with N-dimensional ladder-type
operators associated with the discrete Fourier transform is described,
following an analogy with the canonical commutation relations of the continuous
case. It is found that a Hermitian Toeplitz matrix Z_N, which plays the
role of the identity, is sufficient to satisfy the Jacobi identity and, by solving
some compatibility relations, a family of ladder operators with corresponding
Hamiltonians can be constructed. The behaviour of the matrix Z_N for large
N is elaborated. It is shown that this system can be also realized in terms
of the Heun operator W, associated with the discrete Fourier transform, thus
providing deeper insight on the underlying algebraic structure.

Keywords

ladder operators , Hermitian Toeplitz operator , discrete Fourier transform

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