Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials

Details Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials

2002-01-03

arxiv.org/abs/math-ph/0201006v3

Reviews in Mathematical Physics 14 (2002) 1051-1072

Physics

Mathematical Physics

Corrected version

Scientific paper

10.1142/S0129055X02001491

We consider the Schroedinger operator H 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 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.

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