Precise spectral asymptotics for perturbed magnetic Schrödinger operator
For a Schrödinger operator \(H_B\) with a constant nondegenerate magnetic tensor \(B\), perturbed by an electric potential \(V\) decaying at infinity, two types of spectral asymptotics are considered: 1) a series of eigenvalues of \(H_B+ V\) in a gap of the essential spectrum \(\sigma_{\text{ess}}(H_B)\) of \(H_B\), and 2) the number of eigenvalue branches of a family \(H_B+tV\), crossing an energy level in a gap of \(\sigma_{\text{ess}}(H_B)\), as \(t\to+\infty\) (in the last case, \(V\) is assumed to be nonnegative). The principal terms of the asymptotics, with remainder estimates, which are in certain cases sharp, are computed; for the first problem, under additional conditions of global character, the next term of the asymptotics is computed.
scientific article; zbMATH DE number 1022291
scientific article