Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials

Georgi D. Raikov; Simone Warzel

doi:10.1016/S1631-073X(02)02554-2

Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials

Translated title of the contribution: Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials

Georgi D. Raikov, Simone Warzel

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We consider the Schrödinger operator H(V) on L²(ℝ²) or L²(ℝ³) with constant magnetic field, and a class of electric potentials V which typically decay at infinity exponentially fast or have a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V) near the boundary points of its essential spectrum. If V decays like a 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.

Translated title of the contribution	Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials
Original language	English
Pages (from-to)	683-688
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	335
Issue number	8
DOIs	https://doi.org/10.1016/S1631-073X(02)02554-2
State	Published - 15 Oct 2002
Externally published	Yes

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title = "Spectral asymptotics for magnetic Schr{\"o}dinger operators with rapidly decreasing electric potentials",

abstract = "We consider the Schr{\"o}dinger operator H(V) on L2(ℝ2) or L2(ℝ3) with constant magnetic field, and a class of electric potentials V which typically decay at infinity exponentially fast or have a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V) near the boundary points of its essential spectrum. If V decays like a 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.",

author = "Raikov, {Georgi D.} and Simone Warzel",

note = "Funding Information: Acknowledgements. The authors thank Hajo Leschke and Grigori Rozenblum for stimulating discussions. The financial support of the Chilean Science Foundation Fondecyt under Grants 1020737 and 7020737 is gratefully acknowledged.",

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T1 - Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials

AU - Raikov, Georgi D.

AU - Warzel, Simone

N1 - Funding Information: Acknowledgements. The authors thank Hajo Leschke and Grigori Rozenblum for stimulating discussions. The financial support of the Chilean Science Foundation Fondecyt under Grants 1020737 and 7020737 is gratefully acknowledged.

PY - 2002/10/15

Y1 - 2002/10/15

N2 - We consider the Schrödinger operator H(V) on L2(ℝ2) or L2(ℝ3) with constant magnetic field, and a class of electric potentials V which typically decay at infinity exponentially fast or have a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V) near the boundary points of its essential spectrum. If V decays like a 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.

AB - We consider the Schrödinger operator H(V) on L2(ℝ2) or L2(ℝ3) with constant magnetic field, and a class of electric potentials V which typically decay at infinity exponentially fast or have a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V) near the boundary points of its essential spectrum. If V decays like a 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.

UR - http://www.scopus.com/inward/record.url?scp=0011834034&partnerID=8YFLogxK

U2 - 10.1016/S1631-073X(02)02554-2

DO - 10.1016/S1631-073X(02)02554-2

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VL - 335

SP - 683

EP - 688

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 8

ER -

Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials

Abstract

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