Boundedness of two- and three-body resonances

Erik Balslev; Erik Skibsted

Annales de l'I.H.P. Physique théorique (1985)

  • Volume: 43, Issue: 4, page 369-397
  • ISSN: 0246-0211

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Balslev, Erik, and Skibsted, Erik. "Boundedness of two- and three-body resonances." Annales de l'I.H.P. Physique théorique 43.4 (1985): 369-397. <http://eudml.org/doc/76306>.

@article{Balslev1985,
author = {Balslev, Erik, Skibsted, Erik},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {dilation-analytic resonances; two-body Schrödinger operators; real part of resonance energies},
language = {eng},
number = {4},
pages = {369-397},
publisher = {Gauthier-Villars},
title = {Boundedness of two- and three-body resonances},
url = {http://eudml.org/doc/76306},
volume = {43},
year = {1985},
}

TY - JOUR
AU - Balslev, Erik
AU - Skibsted, Erik
TI - Boundedness of two- and three-body resonances
JO - Annales de l'I.H.P. Physique théorique
PY - 1985
PB - Gauthier-Villars
VL - 43
IS - 4
SP - 369
EP - 397
LA - eng
KW - dilation-analytic resonances; two-body Schrödinger operators; real part of resonance energies
UR - http://eudml.org/doc/76306
ER -

References

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  1. [1] S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa, Class. Sci., Ser. IV, II, 1975, p. 151-218. Zbl0315.47007MR393882
  2. [2] E. Balslev, Analytic scattering theory of two-body Schrödinger operators, J. Funct. Analysis, t. 29, n° 3, 1978, p. 375-396. Zbl0392.47003MR512251
  3. [3] E. Balslev, Decomposition of many-body Schrödinger operators, Comm. Math. Phys. t. 52, 1977, p. 127-146. Zbl0352.35038MR438950
  4. [4] E. Balslev, Analytic scattering theory of quantum-mechanical three-body systems, Ann. Inst. Henri Poincaré, Vol. XXXII, n° 2, 1980, p. 125-160. Zbl0428.47003MR580324
  5. [5] E. Balslev, Resonances in three-body scattering theory, Adv. Appl. Math., t. 5, 1984, p. 260-285. Zbl0617.47008MR755381
  6. [6] E. Balslev and J.M. Combes, Spectral properties of many-body Schrödinger operators with dilation-analytic interactions, Comm. Math. Phys., t. 22, 1971, p. 280-299. Zbl0219.47005MR345552
  7. [7] J. Ginibre and M. Moulin, Hilbert space approach to the quantum mechanical three-body problem, Ann. Inst. H. Poincaré, Vol. XXI, n° 2, 1974, p. 97-145. Zbl0311.47003MR368656
  8. [8] R.J. Iorio and M. O'Carroll, Asymptotic completeness for multiparticle Schrödinger Hamiltonians with weak potentials, Comm. Math. Phys., t. 27, 1972, p. 137-145. MR314392
  9. [9] A. Jensen, Local decay in time of solutions to Schrödinger's equation with dilation-analytic interaction, Manuscripta Math., 1978, t. 25, p. 61-77. Zbl0397.35056MR492959
  10. [10] R. Newton, Scattering theory of waves and particles, 2nd edition, Springer-Verlag, 1982. Zbl0496.47011MR666397
  11. [11] M. Reed and B. Simon, Methods of modern mathematical physics, III and IV. New York, Academic Press, 1979 and 1978. MR529429
  12. [12] B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms, Princeton University Press, 1971. Zbl0232.47053MR455975
  13. [13] B. Simon, Quadratic form techniques and the Balslev-Combes theorem, Comm. Math. Phys., t. 27, 1972, p. 1-12. Zbl0237.35025MR321456
  14. [14] E. Skibsted, Resonances of Schrödinger operators with potentials. V(r) = γrβe-ζrα, β &gt; - 2, ζ &gt; 0 and α &gt; 1, to appear in J. Math. Anal. Appl. Zbl0611.35014MR843011

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