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Article type: Research Article
Authors: Sobolev, Alexander V.
Affiliations: Centre for Mathematical Analysis and Its Applications, University of Sussex, Falmer, Brighton, BN1 9QH, UK. E-mail: [email protected]
Note: [] Author supported by EPSRC under grant B/94/AF/1793.
Abstract: We study the sum of negative eigenvalues M(h,μ) of the Schrödinger operator HV(h,μ) in L2(R3) with a decaying at infinity potential V and a homogeneous magnetic field of intensity μ. The parameter h denotes the Planck constant. Assuming that V has a finite number of Coulomb singularities and is smooth outside them, we establish the two-term asymptotics of M(h,μ) as h→0 and μ→∞. The second term is determined only by the singularities of V and it turns out to be the same as in the case μ=0.
DOI: 10.3233/ASY-1996-13404
Journal: Asymptotic Analysis, vol. 13, no. 4, pp. 393-421, 1996
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