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.
"Semiclassical approximation of the magnetic Schrödinger operator on a strip: dynamics and spectrum." Tunisian J. Math. 2 (1) 197 - 215, 2020. https://doi.org/10.2140/tunis.2020.2.197