Faculty of Physics - University of Bucharest

UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2024-11-24 21:12

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Conference: Bucharest University Faculty of Physics 2015 Meeting

Section: Theoretical Physics and Applied Mathematics

Title:

Finite-dimensional versions of the quantum harmonic oscillator

Authors:

Nicolae COTFAS

Affiliation:

Faculty of Physics, University of Bucharest

E-mail

Keywords:

Abstract:

There exist several remarkable finite-dimensional versions of the harmonic oscillator. They are obtained by using the finite Fourier transform (Fourier oscillator), a finite-difference momentum (Harper oscillator), the unitary irreducible representations of the Lie algebra su(2) (Kravchuk oscillator), the unitary irreducible representations of a deformation of su(2) (Hahn oscillator). We obtain new finite-dimensional versions of the quantum harmonic oscillator by using the coherent state quantization and a finite counterpart, the finite frame quantization. Our approach, obtained by following the analogy with some mathematical formalisms developed around the quantum harmonic oscillator, is based on the finite Heisenberg-Weyl group, some systems of coherent states and some finite frames.