Discrete spectrum asymptotics for the Schrödinger operator with a singular potential and a magnetic field

Reviews in Mathematical Physics

Volumn 8, Issue 6, 1996, Pages 861-903

  Sobolev, A V ^a  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030207808     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X96000305     Document Type: Article

References (15)

1. Sh. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations, Princeton Univ. Press, Princeton, 1982.
2. o-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser, 1996.
3. J. Avron, I. Herbst, and B. Simon, "Schrödinger operators with magnetic fields, I", Duke Math. J. 45(4) (1978) 847-883.
4. M. Sh. Birman and M. Z. Solomyak, "Estimates for number of negative eigenvalues of the Schrödinger operator and its generalizations", Advances in Soviet Mathematics, Vol. 7, ed. M. Sh. Birman, Amer. Math. Soc., 1991, pp. 1-55.
5. A. Bohm, Quantum Mechanics: Foundations and Applications, Springer, 1986.
6. M. Cwickel, "Weak type estimates for singular values and the number of bound states of Schrödinger operators", Ann. of Math. 106 (1977) 93-100.
7. N. Dunford and J. Schwartz, Linear Operators, II, John Wiley & Sons, 1963.
8. V. Ivrii and I. M. Sigal, "Asymptotics of the ground state energies of large Coulomb systems", Ann. of Math. 138 (1993) 243-335.
9. V. Ivrii, "Semiclassical microlocal analysis and precise spectral asymptotics", Ecole Polytechnique, Preprints, Palaiseau, 1991-1992.
10. V. Ivrii, "Estimates for the number of negative eigenvalues of the Schrödinger operator with a strong magnetic field", Soviet Math. Dokl. 36(3) (1988) 561-564.
11. V. Ivrii, "Estimates for the number of negative eigenvalues of the Schrödinger operator with singular potentials", Proc. Int. Congr. Math. Berkeley (1986) 1084-1093.
12. E. H. Lieb, J. P. Solovej, and J. Yngvason, "Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions", Comm. Math. Phys. 161 (1994) 77-124.
13. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. III, Academic Press.
14. A. Sobolev, "Quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a moderate magnetic field", Annales de l'I. H. P. 62, No. 4 (1995) 325-359.
15. A. Sobolev, "The quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a strong homogeneous magnetic field", Duke Math. J. 74(2) (1994) 319-429.