  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.
