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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
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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 periodic Schrödinger operator, semi-classical asymptotics, effective Hamiltonian, asymptotic expansion, spectral shift function
MSC Classifications: 81Q10, 35P20, 47A55, 47N50, 81Q15 show english descriptions Selfadjoint operator theory in quantum theory, including spectral analysis
Asymptotic distribution of eigenvalues and eigenfunctions
Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
Applications in the physical sciences
Perturbation theories for operators and differential equations
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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