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

Georgi D. Raikov·Simone Warzel
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Abstract

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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Georgi D. Raikov, Simone Warzel. 2003-01-10. Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials. https://doi.org/10.1142/s0129055x02001491

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