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Zbl 0732.35079
Horn, Werner
Semi-classical constructions in solid state physics. (English)
[J] Commun. Partial Differ. Equations 16, No.2-3, 255-289 (1991). ISSN 0360-5302; ISSN 1532-4133/e

A Schrödinger equation with weak constant magnetic field is considered. Approximate eigenfunctions are constructed in a neighborhood of a saddle point of the Fermi surface. The construction uses solutions of the Weber equation and complex analysis. The problem was studied for a Fermi surface without stationary points by J. C. Guillot, J. Ralston, E. Trubowitz.
[J.Asch (Berlin)]

MSC 2000:: *35Q40 PDE from quantum mechanics
81Q20 Semi-classical techniques in quantum theory
35C20 Asymptotic expansions of solutions of PDE

Keywords: Schrödinger equation; magnetic field; Approximate eigenfunctions

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