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The non-standard quantum deformation of the (trivially) extended sl(2,R)algebra is used to construct a new quantum deformation of the two-photonalgebra h_6 and its associated quantum universal R-matrix. A deformed one-bosonrepresentation for this algebra is deduced and applied to construct a firstorder deformation of the differential equation that generates the two-photonalgebra eigenstates in Quantum Optics. On the other hand, the isomorphismbetween h_6 and the (1+1) Schr\"odinger algebra leads to a new quantumdeformation for the latter for which a differential-difference realization ispresented. From it, a time discretization of the heat-Schr\"odinger equation isobtained and the quantum Schr\"odinger generators are shown to be symmetryoperators.Comment: 12 pages, LaTe

QUANTUM TWO-PHOTON ALGEBRA FROM NON-STANDARD Uz(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