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 h6 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 h6 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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