Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schr\"odinger equation
Abstract
The non-standard quantum deformation of the (trivially) extended sl(2,R) algebra is used to construct a new quantum deformation of the two-photon algebra h_6 and its associated quantum universal R-matrix. A deformed one-boson representation for this algebra is deduced and applied to construct a first order deformation of the differential equation that generates the two-photon algebra eigenstates in Quantum Optics. On the other hand, the isomorphism between h_6 and the (1+1) Schr\"odinger algebra leads to a new quantum deformation for the latter for which a differential-difference realization is presented. From it, a time discretization of the heat-Schr\"odinger equation is obtained and the quantum Schr\"odinger generators are shown to be symmetry operators.
Cite
@article{arxiv.q-alg/9709009,
title = {Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schr\"odinger equation},
author = {Angel Ballesteros and Francisco J. Herranz and Preeti Parashar},
journal= {arXiv preprint arXiv:q-alg/9709009},
year = {2009}
}
Comments
12 pages, LaTeX