Two-term asymptotics for the sum of eigenvalues of the Schrödinger operator with Coulomb singularities in a homogeneous magnetic field

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