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# Semi-classical Asymptotics for Schrödinger Operator with Oscillating Decaying Potential

Published:2016-05-24
Printed: Dec 2016
• Mouez Dimassi,
Université Bordeaux I, Institut de Mathématiques de Bordeaux, 351, Cours de la Libération, 33405 Talence, France
 Format: LaTeX MathJax PDF

## Abstract

We study the distribution of the discrete spectrum of the Schrödinger operator perturbed by a fast oscillating decaying potential depending on a small parameter $h$.
 Keywords: periodic Schrödinger operator, semi-classical asymptotics, effective Hamiltonian, asymptotic expansion, spectral shift function
 MSC Classifications: 81Q10 - Selfadjoint operator theory in quantum theory, including spectral analysis 35P20 - Asymptotic distribution of eigenvalues and eigenfunctions 47A55 - Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47N50 - Applications in the physical sciences 81Q15 - Perturbation theories for operators and differential equations

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