Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010Spectral problems. Issue dedicated to the memory of M. Birman
|Page(s)||32 - 53|
|Published online||12 May 2010|
Discrete Spectrum of the Periodic Schrödinger Operator with a Variable Metric Perturbed by a Nonnegative Potential
Department of Physics, St. Petersburg State University,
Ul’yanovskaya 3, Petrodvorets,
St. Petersburg, 198504, RUSSIA
* E-mail: email@example.com
We study discrete spectrum in spectral gaps of an elliptic periodic second order differential operator in L2(ℝd) perturbed by a decaying potential. It is assumed that a perturbation is nonnegative and has a power-like behavior at infinity. We find asymptotics in the large coupling constant limit for the number of eigenvalues of the perturbed operator that have crossed a given point inside the gap or the edge of the gap. The corresponding asymptotics is power-like and depends on the observation point.
Mathematics Subject Classification: 47F05 / 47G10
Key words: periodic Schrödinger operator / discrete spectrum / spectral gaps / asymptotics in the large coupling constant limit.
© EDP Sciences, 2010
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