Tunisian Journal of Mathematics
- Tunisian J. Math.
- Volume 2, Number 1 (2020), 197-215.
Semiclassical approximation of the magnetic Schrödinger operator on a strip: dynamics and spectrum
In the semiclassical regime (i.e., ), we study the effect of a slowly varying potential on the magnetic Schrödinger operator on a strip . The potential is assumed to be smooth. We derive the semiclassical dynamics and we describe the asymptotic structure of the spectrum and the resonances of the operator for small enough. All our results depend on the eigenvalues corresponding to on with Dirichlet boundary condition.
Tunisian J. Math., Volume 2, Number 1 (2020), 197-215.
Received: 10 October 2018
Revised: 17 November 2018
Accepted: 2 December 2018
First available in Project Euclid: 2 April 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47N50: Applications in the physical sciences 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis 81Q15: Perturbation theories for operators and differential equations
Dimassi, Mouez. Semiclassical approximation of the magnetic Schrödinger operator on a strip: dynamics and spectrum. Tunisian J. Math. 2 (2020), no. 1, 197--215. doi:10.2140/tunis.2020.2.197. https://projecteuclid.org/euclid.tunis/1554170465