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.
ladder operators Hermitian Toeplitz operator discrete Fourier transform
Birincil Dil | İngilizce |
---|---|
Konular | Matematiksel Yöntemler ve Özel Fonksiyonlar |
Bölüm | Articles |
Yazarlar | |
Erken Görünüm Tarihi | 10 Ekim 2024 |
Yayımlanma Tarihi | |
Gönderilme Tarihi | 10 Nisan 2024 |
Kabul Tarihi | 24 Mayıs 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 6 Sayı: 2 |
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ISSN 2667-7660