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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-24 23:59 |
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Conference: Bucharest University Faculty of Physics 2012 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
Finite-dimensional quantum systems
and the discrete-continuous transition
Authors:
N. COTFAS
Affiliation:
Department of Theoretical Physics, Mathematics, Optics, Plasma, Lasers, Faculty of Physics,University of Bucharest
E-mail
ncotfas@yahoo.com
Keywords:
Finite Fourier transform, Finite quantum systems, finite systems of coherent states
Abstract:
Consider a d-dimesional Hilbert space, a fixed orthonormal basis and the images of the elements of this basis through the finite Fourier which form a second orthonormal basis. By using the elements of the two orthonormal bases as eigenvectors we define the position and momentum operators. The corresponding displacement operators define a projective representation of the finite Weyl group which allows us to generate a finite system of coherent states. We investigate the occurrence of revivals in the case of free evolution and in the case of a harmonic oscillator Hamiltonian. In all cases, a particular emphasis is put on the recovery of the known continuous-limit results when the dimension d of the system increases.
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