Space-Time Lattice for Operator SCHRÖDINGER Equation

We propose a spatio-temporal discretization of the Schrödinger equation for field operators of noninteracting bosons. The scheme, being based on the associated space of the creation and annihilation operators and on discretization of the Schrödinger equation possesses all relevant properties of the underline continuum model. The discretization appears to be a linear part of an integrable discretization of classical nonlinear Schrödinger equation which allows one to obtain some exact solutions.