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MP: Theoretische und Mathematische Grundlagen der Physik

MP 10: Sonstiges

MP 10.2: Fachvortrag

Freitag, 19. März 1999, 16:15–16:30, MA1

Schrödinger equation as the universal continuum limit of nonrelativistic hopping on a cubic spatial lattice — •Lutz Polley — FB Physik, Universität, 26111 Oldenburg

The Schrödinger equation with scalar and vector potentials emerges as the continuum limit of any coherent hopping process on a lattice (where position eigenstates spread out to neighbouring sites after a time step) providing that the process is homogeneous in quadratic order of the inverse lattice spacing, and inhomogeneous in first order. Higher-than-next neighbours are taken into account, but it is assumed that the 2nd moment of the hopping amplitudes is finite, due to which the process is nonrelativistic. The classical Hamiltonian is not used in the argument.