Schroedinger equation as the universal continuum limit of nonrelativistic coherent hopping on a cubic spatial lattice
Lutz Polley
Abstract
The Schroedinger equation with scalar and vector potentials is the continuum limit of any coherent hopping process (where position eigenstates superpose with neighbouring eigenstates after a time step) whose hopping amplitudes are homogeneous in quadratic order of the inverse lattice spacing, inhomogeneous in first order, and satisfying a summability condition with respect to higher-than-next neighbours.
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