Journal of Spectral Theory


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Volume 3, Issue 4, 2013, pp. 517–534
DOI: 10.4171/JST/54

Published online: 2013-10-23

The spectral density of the scattering matrix of the magnetic Schrödinger operator for high energies

Daniel Bulger[1] and Alexander Pushnitski[2]

(1) King's College London, UK
(2) King's College London, UK

The scattering matrix of the Schrödinger operator with smooth short-range electric and magnetic potentials is considered. The asymptotic density of the eigenvalues of this scattering matrix in the high energy regime is determined. An explicit formula for this density is given. This formula involves only the magnetic vector-potential.

Keywords: Scattering matrix, scattering phase, Schrödinger operator, magnetic field, spectral density

Bulger Daniel, Pushnitski Alexander: The spectral density of the scattering matrix of the magnetic Schrödinger operator for high energies. J. Spectr. Theory 3 (2013), 517-534. doi: 10.4171/JST/54