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Properties of finite Gaussians and the discrete-continuous transition

Domenii publicaţii > Fizica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Nicolae Cotfas and Daniela Dragoman

Editorial: IOP PUBLISHING, J. Phys. A: Math. Theor. , 45, p.425305 , 2012.

Rezumat:

Weyl’s formulation of quantum mechanics opened the possibility of
studying the dynamics of quantum systems both in infinite-dimensional
and finite-dimensional systems. Based on Weyl’s approach, generalized by
Schwinger, a self-consistent theoretical framework describing physical systems
characterized by a finite-dimensional space of states has been created. The
used mathematical formalism is further developed by adding finite-dimensional
versions of some notions and results from the continuous case. Discrete versions
of the continuous Gaussian functions have been defined by using the Jacobi
theta functions. We continue the investigation of the properties of these finite
Gaussians by following the analogy with the continuous case. We study the
uncertainty relation of finite Gaussian states, the form of the associatedWigner
quasi-distribution and the evolution under free-particle and quantum harmonic
oscillatorHamiltonians. 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.

Cuvinte cheie: Finite Gaussians,finite oscilattor,discrete Wigner function

URL: http://iopscience.iop.org/1751-8121/45/42/425305