On the number of negative eigenvalues for the two-dimensional magnetic Schrödinger operator. (English) Zbl 0920.35101

Buslaev, V. (ed.) et al., Differential operators and spectral theory. M. Sh. Birman’s 70th anniversary collection. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 189(41), 205-217 (1999).
Summary: An estimate on the number of negative eigenvalues of the magnetic Schrödinger operator in two dimensions is obtained. It extends to the magnetic case an earlier “nonmagnetic” result by M. Birman and V. Borzov. The estimate is applied to the study of the asymptotic behavior of eigenvalues for strong electric fields.
For the entire collection see [Zbl 0911.00011].


35P15 Estimates of eigenvalues in context of PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
47F05 General theory of partial differential operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis