Bound states and scattering states for time periodic hamiltonians

Kenji Yajima; Hitoshi Kitada

Annales de l'I.H.P. Physique théorique (1983)

  • Volume: 39, Issue: 2, page 145-157
  • ISSN: 0246-0211

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Yajima, Kenji, and Kitada, Hitoshi. "Bound states and scattering states for time periodic hamiltonians." Annales de l'I.H.P. Physique théorique 39.2 (1983): 145-157. <http://eudml.org/doc/76214>.

@article{Yajima1983,
author = {Yajima, Kenji, Kitada, Hitoshi},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {completeness of the modified wave operators; characterization of the bound and scattering states in terms of the spectral properties of the Floquet operator; propagator; Schrödinger equation; periodic Hamiltonian; spectral subspace},
language = {eng},
number = {2},
pages = {145-157},
publisher = {Gauthier-Villars},
title = {Bound states and scattering states for time periodic hamiltonians},
url = {http://eudml.org/doc/76214},
volume = {39},
year = {1983},
}

TY - JOUR
AU - Yajima, Kenji
AU - Kitada, Hitoshi
TI - Bound states and scattering states for time periodic hamiltonians
JO - Annales de l'I.H.P. Physique théorique
PY - 1983
PB - Gauthier-Villars
VL - 39
IS - 2
SP - 145
EP - 157
LA - eng
KW - completeness of the modified wave operators; characterization of the bound and scattering states in terms of the spectral properties of the Floquet operator; propagator; Schrödinger equation; periodic Hamiltonian; spectral subspace
UR - http://eudml.org/doc/76214
ER -

References

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  1. [1] W.O. Amrein and V. Georgescu, On the characterization of bound states and scattering states in quantum mechanics, Helv. Phys. Acta, t. 46, 1973, p. 635-657. MR363267
  2. [2] V. Enss, Asymptotic completeness for quantum mechanical potential scattering, Commun. Math. Phys., t. 61, 1978, p. 285-291. Zbl0389.47005MR523013
  3. [3] J.S. Howland, Stationary scattering theory for time-periodic Hamiltonians, Math. Ann., t. 207, 1974, p. 315-335. Zbl0261.35067MR346559
  4. [4] J.S. Howland, Scattering theory for Hamiltonians periodic in time, Indiana Univ. Math. J., t. 28, 1979, p. 471-494. Zbl0444.47010MR529679
  5. [5] Kato T., Wave operators and similarity for some nonselfadjoint operators, Math. Ann., t. 162, 1966, p. 258-279. Zbl0139.31203MR190801
  6. [6] H. Kitada and K. Yajima, A scattering theory for time-dependent long range potentials, Duke Math. J., t. 49, 1982, p. 341-376. Zbl0499.35087MR659945
  7. [7] S.T. Kuroda, Scattering theory for differential operators, I, Operator theory, J. Math. Soc. Japan, t. 25, 1973, p. 73-104. Zbl0245.47006MR326435
  8. [8] S.T. Kuroda, An introduction to scattering theory, Aarhus Univ. Lecture Notes Ser., t. 51, 1978. Zbl0407.47003MR528757
  9. [9] T. Kisynski, Sur les opérateurs de Green des problèmes de Cauchy abstracts, Studia Math., t. 23, 1964, p. 285-328. Zbl0117.10202MR161185
  10. [10] M. Reed and B. Simon, Methods of moder mathematical physics, III, Scattering theory, Academic Press, New York- San Francisco-London, 1979. Zbl0405.47007MR529429
  11. [11] D. Ruelle, A remark on bound states in potential scattering theory, Nuovo Cimento, t. 59 A, 1969, p. 655-662. MR246603
  12. [12] B. Simon, Quantum mechanics for Hamiltonians defined as quadratic forms, Princeton Univ. Press, Princeton, N. J., 1971. Zbl0232.47053MR455975
  13. [13] K. Yajima, Scattering theory for Schrödinger equations with potentials periodic in time, J. Math. Soc. Japan, t. 29, 1977, p. 729-743. Zbl0356.47010MR470525
  14. [14] K. Yajima, Resonances for the AC-Stark effect, Commun. Math. Phys., t. 87, 1982, p. 331-352. Zbl0538.47010MR682111
  15. [15] G. Hagedorn, An analog of the Rage Theorem for the impact parameter approximation to three particle scattering, Annales de l'IHP, t. 38, 1983, p. 59-69. Zbl0517.47009MR700700

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