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

Angel Ballesteros·Francisco J. Herranz·Preeti Parashar
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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) Schrödinger 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-Schrödinger equation is obtained and the quantum Schrödinger generators are shown to be symmetry operators.

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Angel Ballesteros, Francisco J. Herranz, Preeti Parashar. 1997-09-03. Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schrödinger equation. https://doi.org/10.1142/s0217732398001315

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