3 papers
math-ph2004★ 18 cited
The Spectral Asymptotics of the Two-Dimensional Schrödinger operator with a Strong Magnetic Field
Jochen Bruening, Sergey Dobrokhotov, Konstantin Pankrashkin
We consider the spectral problem for the two-dimensional Schrödinger operator for a charged particle in strong uniform magnetic and periodic electric fields. The related classical…
math-ph2004★ 15 cited
On-diagonal singularities of the Green functions for Schroedinger operators
Jochen Bruening, Vladimir Geyler, Konstantin Pankrashkin
We investigate the behavior of the Green functions of Schroedinger operators near the diagonal. The only non-trivial cases, where the on-diagonal singularities are non-zero and do…
math-ph2004★ 3 cited
On semiclassical dispersion relations of Harper-like operators
Konstantin Pankrashkin
We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral regio…