An upper bound for the local time-decay of scattering solutions for the Schrödinger equation with Coulomb potential

Hans L. Cycon

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

  • Volume: 39, Issue: 4, page 385-392
  • ISSN: 0246-0211

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Cycon, Hans L.. "An upper bound for the local time-decay of scattering solutions for the Schrödinger equation with Coulomb potential." Annales de l'I.H.P. Physique théorique 39.4 (1983): 385-392. <http://eudml.org/doc/76219>.

@article{Cycon1983,
author = {Cycon, Hans L.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Dollard-wave operator; Coulomb-Schrödinger operator; Hilbert space; large-time decay},
language = {eng},
number = {4},
pages = {385-392},
publisher = {Gauthier-Villars},
title = {An upper bound for the local time-decay of scattering solutions for the Schrödinger equation with Coulomb potential},
url = {http://eudml.org/doc/76219},
volume = {39},
year = {1983},
}

TY - JOUR
AU - Cycon, Hans L.
TI - An upper bound for the local time-decay of scattering solutions for the Schrödinger equation with Coulomb potential
JO - Annales de l'I.H.P. Physique théorique
PY - 1983
PB - Gauthier-Villars
VL - 39
IS - 4
SP - 385
EP - 392
LA - eng
KW - Dollard-wave operator; Coulomb-Schrödinger operator; Hilbert space; large-time decay
UR - http://eudml.org/doc/76219
ER -

References

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  1. [1] W.O. Amrein, M.J. Jauch, K.B. Sinha, Scattering theory in Quantum Mechanics, Benjamin, Reading, Mass, 1977. Zbl0376.47001MR495999
  2. [2] H.L. Cycon, Absence of singular continuous spectrum for two body Schrödinger operators with long-range potentials (a new proof). Proc. of Roy. Soc. of Edinburgh, t. 94 A, 1983, p. 61-69. Zbl0523.35034MR700499
  3. [3] J.D. Dollard, Quantum mechanical scattering theory for short-range and Coulomb interactions, Rocky Mountain J. of Math., t. 1, n° 1, 1971, p. 5-88. Zbl0226.35074MR270673
  4. [4] A. Jensen, Local decay in time of solutions to Schrödinger's equation with a dilatation–analytic interaction, manuscripta math., t. 25, 1978, p. 61-77. Zbl0397.35056MR492959
  5. [5] A. Jensen, Spectral properties of Schrödinger operators and time-decay of the wave functions; results in L2(Rm), m ≥ 5, Duke Math. J., t. 47, n° 1, 1980, p. 57-80. Zbl0437.47009MR563367
  6. [6] A. Jensen, T. Kato, Spectral properties of Schrödinger operators and time decay of the wave functions, Duke Math. J., t. 46, n° 3, 1979, p. 583-611. Zbl0448.35080MR544248
  7. [7] T. Kato, Perturbation theory for linear operators, Berlin, Heidelberg, New York, Springer, 1966. Zbl0148.12601MR203473
  8. [8] H. Kitada, Time decay of the high energy part of the solutionfor a Schrödinger equation, preprint University of Tokyo, 1982. MR743522
  9. [9] M. Murata, Scattering solutions decay at least logarithmically, Proc. Jap. Ac., t. 54, Ser. A, 1978, p. 42-45. Zbl0395.35022MR486379
  10. [10] J. Rauch, Local decay of Scattering solutions to Schrödinger's equation, Comm. Math. Phys., t. 61, 1978, p. 149-168. Zbl0381.35023MR495958
  11. [11] M. Reed, B. Simon, Methods of modern mathematical physics III, Scattering theory, Acad. press, 1979. Zbl0405.47007MR529429
  12. [12] M. Reed, B. Simon, Methods of modern mathematical physics IV. Analysis of operators, Acad. press, 1978. Zbl0401.47001MR493421

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