Cluster properties of one particle Schrödinger operators. II

Reviews in Mathematical Physics

Volumn 10, Issue 5, 1998, Pages 627-683

  Kostrykin, V ^a   Schrader, R ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040944352     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X98000203     Document Type: Article

References (44)

1. S. Albeverio, F. Gesztesy and R. Høegh-Krohn, "The low energy expansion in nonrelativistic scattering theory", Ann. Inst. Henri Poincaré, Physique théorique 37 (1982) 1-28.
2. S. Albeverio, F. Gesztesy, R. Høegh-Krohn and H. Holden, Solvable Models in Quantum Mechanics, Springer, Berlin, 1988.
3. P. Aventini and R. Seiler, "On the electronic spectrum of the diatomic molecular ion", Commun. Math. Phys. 41 (1975) 119-134.
4. M. Sh. Birman and M. G. Krein, "On the theory of wave operators and scattering operators", Sov. Math. - Dokady 3 (1962) 740-744.
5. M. Sh. Birman and D. R. Yafaev, "The spectral shift function. Work by M. G. Krein and its further development", St. Petersburg Math. J. 4 (1993) 833-870.
6. D. Bollé and S. F. J. Wilk, "Low-energy sum rules for two-particle scattering", J. Math. Phys. 24 (1983) 1555-1563.
7. 3", Ann. scient. Éc. Norm. Sup. 14 (1981) 27-39.
8. J. M. Combes and R. Seiler, "Regularity and asymptotic properties of the discrete spectrum of the electronic Hamiltonians", Int. J. Quantum Chem. 14 (1978) 213-229.
9. E. B. Davies, "The twisting trick for double well Hamiltonians", Commun. Math. Phys. 85 (1982) 471-479.
10. T. Dreyfus, "The determinant of the scattering matrix and its relation to the number of eigenvalues", J. Math. Anal. Appl. 64 (1978) 114-134.
11. T. Dreyfus, "The number of states bound by non-central potentials", Helv. Phys. Acta 51 (1978) 321-329.
12. V. Efimov, "Energy levels arising from resonant two-body forces in a three-body system", Phys. Lett. B33 (1970) 563-564.
13. R. Geisler, V. Kostrykin and R. Schrader, "Concavity properties of Krein's spectral shift function", Rev. Math. Phys. 7 (1995) 161-181.
14. L. Guillopé, "Asymptotique de la phase de diffusion pour l'opérateur de Schrödinger avec potentiel", C. R. Acad. Sc. Paris, Série I 293 (1991) 601-603.
15. E. M. Harrell, "Double wells", Commun. Math. Phys. 75 (1980) 239-261.
16. K. Hepp, "Spatial cluster decomposition properties of the S-matrix", Helv. Phys. Acta 37 (1964) 659-662.
17. R. Høegh-Krohn and M. Mebkhout, "The 1/r expansion for the critical multiple well problem", Commun. Math. Phys. 91 (1983) 65-73.
18. H. Holden, R. Høegh-Krohn and M. Mebkhout, "The short-range expansion for multiple well scattering theory", J. Math. Phys. 26 (1985) 145-151.
19. W. Hunziker, "Cluster properties of multiparticle systems", J. Math. Phys. 6 (1965) 6-10.
20. W. Hunziker, "Mathematical theory of multi-particle quantum systems", in Quantum Theory and Statistical Physics", eds. A. O. Barut and W. E. Brittin, Lectures in Theoretical Physics, Gordon and Breach, New York, 1968, pp. 1-48.
21. A. Jensen and T. Kato, "Spectral properties of Schrödiger operators and time-decay of the wave functions", Duke Math. J. 46 (1979) 583-611.
22. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966.
23. T. Kato, "Monotonicity theorem in scattering theory", Hadronic J. 1 (1978) 134-154.
24. M. Klaus and B. Simon, "Binding of Schrödinger particles through conspirancy of potential wells", Ann. Inst. H. Poincaré, Phys. Theor. 30 (1979) 83-87.
25. M. Klaus, "Some remarks on double - wells in one and three-dimensions", Ann. Inst. H. Poincaré, Phys. Theor. 34 (1981) 405-417.
26. I. V. Komarov and S. Yu. Slavyanov, "The two Coulomb problem at large center separation", J. Phys. B: Atom. Molec. Phys. 1 (1968) 1066-1072.
27. V. Kostrykin and R. Schrader, "Cluster properties of one particle Schrödinger operators", Rev. Math. Phys. 6 (1994) 833-853.
28. M. G. Krein, "On a trace formula in perturbation theory", Matem. Sbornik 33 (1953) 597-626 (in Russian).
29. M. G. Krein, "Perturbation determinants and a formula for the traces of unitary and self-adjoint operators", Sov. Math. - Doklady 3 (1962) 707-710.
30. E. H. Lieb and B. Simon, "Monotonicity of the electronic contribution to the Born-Oppenheimer energy", J. Phys. B: Atom. Molec. Phys. 11 (1978) L537-L542.
31. J. D. Morgan III and B. Simon, "Behavior of molecular potential energy curves for large nuclear separations", Int. J. Quantum Chem. 17 (1980) 1143-1166.
32. R. G. Newton, "Noncentral potentials: The generalized Levinson theorem and the structure of the spectrum", J. Math. Phys. 18 (1977) 1348-1357.
33. R. G. Newton, Scattering Theory of Waves and Particles, Springer, New York, 1982.
34. Yu. N. Ovchinnikov and I. M. Sigal, "Number of bound states of three-body systems and Efimov's effect", Ann. Phys. 123 (1979) 274-295.
35. L. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators, Springer, Berlin, 1992.
36. M. Reed and B. Simon, Methods of Modern Mathematical Physics, II: Fourier Analysis, Self-Adjointness, Academic Press, New York, 1975.
37. M. Reed and B. Simon, Methods of Modern Mathematical Physics, III: Scattering Theory, Academic Press, New York, 1979.
38. M. Reed and B. Simon, Methods of Modern Mathematical Physics, IV: Analysis of Operators, Academic Press, New York, 1978.
39. R. Schrader, "High energy behaviour for non-relativistic scattering by stationary external metrics and Yang-Mills potentials", Z. Phys. C: Particles and Fields 4 (1980) 27-36.
40. P. N. Shivakumar and R. Wong, "Asymptotic expansion of multiple Fourier transforms", SIAM J. Math. Anal. 10 (1979) 1095-1104.
41. B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms, Princeton Univ. Press, Princeton, 1971.
42. B. Simon, Trace Ideals and Their Applications, Cambridge Univ. Press, Cambridge, 1979.
43. H. Tamura, "Existence of bound states for double well potentials and the Efimov effect", in Functional-Analytic Methods for Partial Differential Equations, eds. H. Fujita, T. Ikebe, and S. T. Kuroda, pp. 173-186. Lecture Notes in Mathematics, Vol. 1450, Springer, Berlin, 1990.
44. H. Tamura, "The Efimov effect of three-body Schrödinger operators: Asymptotics for the number of negative eigenvalues", Nagoya Math. J. 130 (1993) 55-83.