Sobolev, A. V. Asymptotic behavior of the energy levels of a quantum particle in a homogeneous magnetic field, perturbed by a decreasing electric field. I. (English. Russian original) Zbl 0643.35028 J. Sov. Math. 35, 2201-2212 (1986); translation from Probl. Mat. Anal. 9, 67-84 (1984). One investigates the bound states \(E_ n\), situated to the left of the boundary of the continuous spectrum. Under the assumption that the potential is nonpositive and has at infinity a power type asymptotics, one computes the principal term of the asymptotics \(E_ n\) as \(n\to \infty\). One does not assume the axial symmetry of the potential of the electric field. Cited in 1 ReviewCited in 13 Documents MSC: 35J10 Schrödinger operator, Schrödinger equation 35P05 General topics in linear spectral theory for PDEs Keywords:quantum particle; decreasing electric field; Schrödinger operator; homogeneous magnetic field; bound states; potential; power type asymptotics; principal term × Cite Format Result Cite Review PDF Full Text: DOI References: [1] L. D. Landau and E. M. Lifshits, Quantum Mechanics. Nonrelativistic Theory, Pergamon (1977). [2] J. Avron, I. Herbst, and B. Simon, ?Schrödinger operators with magnetic fields. I. General interactions,? Duke Math. J.,45, No. 4, 847?883 (1978). · Zbl 0399.35029 · doi:10.1215/S0012-7094-78-04540-4 [3] S. N. Solnyshkin, ?The asymptotic behavior of the energy of bound states of the Schrö-dinger operator in the presence of electric and homogeneous magnetic fields,? Probl. Mat. Fiz., No. 10, 266?278 (1982). · Zbl 0513.35012 [4] M. Sh. Birman and M. Z. Solomyak, ?Quantitative analysis in Sobolev’s imbedding theorems and applications to spectral theory,? ins Proc. Tenth Summer Math. School, 1972, Izd. Inst. Mat. Akad. Nauk UkrSSR, Kiev (1974), pp. 5?189. [5] M. Sh. Birman and M. Z. Solomyak, ?Estimates for the singular numbers of integral operators,? Usp. Mat. Nauk,32, No. 1 (193), 17?84 (1977). · Zbl 0376.47023 [6] M. Sh. Birman and M. Z. Solomyak, ?The asymptotic behavior of the spectrum of weakly polar integral operators,? Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 5, 1142?1158 (1970). · Zbl 0261.47027 [7] M. Sh. Birman and M. Z. Solomyak, ?The asymptotic behavior of the spectrum of pseudodifferential operators with anisotropically homogeneous symbols,? Vestn. Leningr. Univ., No. 13, 13?21 (1977). · Zbl 0377.47033 [8] I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonself-Adjoint Operators, Amer. Math. Soc., Providence (1969). · Zbl 0181.13503 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.