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Absence of singular continuous spectrum in $N$-body quantum systems
Author(s):
P.
Perry;
I. M.
Sigal;
B.
Simon
Journal:
Bull. Amer. Math. Soc.
3
(1980),
1019-1023.
MSC (1970):
Primary 81A81;
Secondary 35P05
MathSciNet review:
585181
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References:
- 1.
- Balslev and J. M. Combes, Spectral properties of Schrödinger Hamiltonians with dilation analytic potentials, Comm. Math. Phys. 22 (1971), 280-294. MR 345552
- 2.
- M. Combescure and J. Ginibre, On the negative point spectrum of quantum mechanical three-body systems, Ann. Phys. 101 (1976), 355-379. MR 438951
- 3.
- L. D. Faddeev, Mathematical aspects of the three body problem in the quantum theory of scattering, Israel Program for Scientific Translation, Jerusalem, 1965. MR 221828
- 4.
- G. A. Hagedorn, Asymptotic completeness for a class of four particle Schrödinger operators, Bull. Amer. Math. Soc. 84 (1978), 155-156; Asymptotic completeness for classes of two, three, and four particle Schrödinger operators, Trans. Amer. Math. Soc. 258 (1980), 1-75. MR 496030
- 5.
- R. J. Iorio and M. O'Carrol, Asymptotic completeness for multiparticle Schrödinger operators with weak potentials, Comm. Math. Phys. 27 (1972), 137-149. MR 314392
- 6.
- R. Lavine, Commutators and scattering theory, I. Repulsive interactions, Comm. Math. Phys. 20 (1971), 301-323; Completeness of the wave operators in the repulsive N-body problem, J. Math. Phys. 14 (1973), 376-379. MR 293945
- 7.
- M. Loss and I. M. Sigal, Many body scattering with quasibound states (in preparation).
- 8.
- E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys. (to appear). MR 603501
- 9.
- P. A. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators (in preparation).
- 10.
- M. Reed and B. Simon, Methods of modern mathematical physics. III. Scattering theory, Academic Press, New York, 1979. MR 751959
- 11.
- M. Reed and B. Simon, Methods of modem mathematical physics. IV. Analysis of operators, Academic Press, New York, 1978. MR 493421
- 12.
- I. M. Sigal, Mathematical foundations of quantum scattering theory for multiparticle systems, Mem. Amer. Math. Soc. No. 209 (1978). MR 508478
- 13.
- I. M. Sigal, On quantum mechanics of many-body systems with dilation-analytic potentials, Bull. Amer. Math. Soc. 84 (1978), 152-154; Scattering theory for multiparticle systems. I, II, (preprint) ETH-Zürich, 1977-1978 (an expanded version will appear in the Springer Lecture Notes in Mathematics). MR 459410
- 14.
- B. Simon, Geometric methods in multiparticle quantum systems, Comm. Math. Phys. 55 (1977), 259-274. MR 496073
- 15.
- D. R. Yafaev, On the point spectrum in the quantum-mechanical many-body problem, Math. USSR Izv. 10 (1976), 861-896.
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Additional Information:
DOI:
10.1090/S0273-0979-1980-14838-7
PII:
S 0273-0979(1980)14838-7
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