- 02-349 Georgi D. Raikov, Simone Warzel
- Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials
Aug 16, 02
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Abstract. We consider the Schroedinger operator H(V) on L^2(R^2) or L^2(R^3)
with constant magnetic field, and electric potential V which typically decays at infinity exponentially fast or has a compact support.
We investigate the asymptotic behaviour of the discrete spectrum of H(V)
near the boundary points of its essential spectrum. If the decay
of V is Gaussian or faster, this behaviour is non-classical in the
sense that it is not described by the quasi-classical formulas known
for the case where V admits a power-like decay.