Perturbations of embedded eigenvalues for a magnetic Schrodinger operator on a cylinder

作者：Laptev Ari^*; Sasane Sara Maad

来源：Journal of Mathematical Physics, 2017, 58(1): 012105.

DOI：10.1063/1.4974360

Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this paper, we study a perturbation problem for embedded eigenvalues for a magnetic Schrodinger operator, when the underlying domain is a cylinder. The magnetic potential is C-2 with an algebraic decay rate as the unbounded variable of the cylinder tends to +/-infinity. In particular, no analyticity of the magnetic potential is assumed. We also assume that the embedded eigenvalue of the unperturbed problem is not the square of an integer, thus avoiding the thresholds of the continuous spectrum of the unperturbed operator. We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension. Published by AIP Publishing.

• 出版日期2017-1