## Oscillatory eigenvalue branches for Schrödinger operators with strongly coupled magnetic fields.(English)Zbl 0922.35104

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), 93-104 (1999).
Summary: We consider a (periodic) Schrödinger operator with a spectral gap, perturbed by a magnetic field of compact support. Here, it is our aim to produce examples where an eigenvalue branch inside the gap approaches a nonconstant periodic function as the coupling constant tends to infinity. The two cases where the total magnetic flux is zero or nonzero have to be treated differently. For comparison reasons, we include a brief discussion of monotonicity properties of eigenvalue branches in the case where the perturbation is given by an electric potential of compact support.
For the entire collection see [Zbl 0911.00011].

### MSC:

 35P15 Estimates of eigenvalues in context of PDEs 35J10 Schrödinger operator, Schrödinger equation 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis

### Keywords:

periodic Schrödinger operator