Schroedinger equation as the universal continuum limit of nonrelativistic coherent hopping on a cubic spatial lattice

Details Schroedinger equation as the universal continuum limit of nonrelativistic coherent hopping on a cubic spatial lattice Schroedinger equation as the universal continuum limit of nonrelativistic coherent hopping on a cubic spatial lattice

1998-11-18

arxiv.org/abs/quant-ph/9811048v2

Physics

Quantum Physics

6 pages, LaTeX; Introduction extended with reference to quantum lattice-gas models

Scientific paper

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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