Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schrödinger equation

Details Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schrödinger equation Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schrödinger equation

1997-09-03

arxiv.org/abs/q-alg/9709009v1

Mod. Phys. Lett. A13 (1998) 1241-1252

Mathematics

Quantum Algebra

12 pages, LaTeX

Scientific paper

10.1142/S0217732398001315

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.

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