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Periodic homogenization of Schrödinger type equations with rapidly oscillating potential. (English) Zbl 1352.35008

Summary: This paper is devoted to the homogenization of Schrödinger type equations with periodically oscillating coefficients of the diffusion term, and a rapidly oscillating periodic potential. One convergence theorem is proved and we derive the macroscopic homogenized model. Our approach is the well known two-scale convergence method.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B40 Asymptotic behavior of solutions to PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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