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Semi-classical asymptotics in solid state physics (1988)

Guillot, J. C. ; Ralston, J. ; Trubowitz, E.

Springer

Communications in mathematical physics 116 (1988), S. 401-415

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract This article studies the Schrödinger equation for an electron in a lattice of ions with an external magnetic field. In a suitable physical scaling the ionic potential becomes rapidly oscillating, and one can build asymptotic solutions for the limit of zero magnetic field by multiple scale methods from “homogenization.” For the time-dependent Schrödinger equation this construction yields wave packets which follow the trajectories of the “semiclassical model.” For the time-independent equation one gets asymptotic eigenfunctions (or “quasimodes”) for the energy levels predicted by Onsager's relation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01229201

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