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Semi-classical constructions in solid state physics. (English) Zbl 0732.35079

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.
Reviewer: J.Asch (Berlin)

MSC:

35Q40 PDEs in connection with quantum mechanics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35C20 Asymptotic expansions of solutions to PDEs
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