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On spectral properties of adiabatically perturbed Schrödinger operators with periodic potentials. (English) Zbl 0739.35053
Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1990-1991, No.XXIII, 15 p. (1991).
Summary: We describe the asymptotic structure of the spectrum and the resonances of the equation \(-\psi_{xx}+V(\varepsilon x,x)\psi=E\psi\), where \(V(\xi,x)\) is a periodic function of the second variable and \(\varepsilon\) is a small parameter.

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
Keywords:
spectrum; resonances
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