Existence of the time evolution for Schrödinger operators with time dependent singular potentials
Annales de l'I.H.P. Physique théorique (1986)
- Volume: 44, Issue: 2, page 155-171
- ISSN: 0246-0211
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topWüller, Ulrich. "Existence of the time evolution for Schrödinger operators with time dependent singular potentials." Annales de l'I.H.P. Physique théorique 44.2 (1986): 155-171. <http://eudml.org/doc/76315>.
@article{Wüller1986,
author = {Wüller, Ulrich},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Schrödinger equation; propagator; Coulomb potential},
language = {eng},
number = {2},
pages = {155-171},
publisher = {Gauthier-Villars},
title = {Existence of the time evolution for Schrödinger operators with time dependent singular potentials},
url = {http://eudml.org/doc/76315},
volume = {44},
year = {1986},
}
TY - JOUR
AU - Wüller, Ulrich
TI - Existence of the time evolution for Schrödinger operators with time dependent singular potentials
JO - Annales de l'I.H.P. Physique théorique
PY - 1986
PB - Gauthier-Villars
VL - 44
IS - 2
SP - 155
EP - 171
LA - eng
KW - Schrödinger equation; propagator; Coulomb potential
UR - http://eudml.org/doc/76315
ER -
References
top- [1] J.B. Delos, Theory of electronic transitions in slow atomic collisions. Rev. Mod. Phys., t. 53, 1981, p. 287-357.
- [2] G.A. Hagedorn, An analog of the RAGE Theorem for the impact parameter approximation to three particle scattering. Ann. Inst. H. Poincaré, t. A 38, 1983, p. 59-68. Zbl0517.47009MR700700
- [3] G.C. Hegerfeld, Remarks on causality, localization and spreading of wave packets. Phys. Rev. D., t. 22, 1980, p. 377-384. MR578960
- [4] T. Kato, Integration of the equation of evolution in a Banach space. J. Math. Soc. Japan, t. 5, 1953, p. 208-234. Zbl0052.12601MR58861
- [5] T. Kato, On linear differential equations in Banach spaces. Comm. Pure Appl. Math., t. 9, 1956, p. 479-486. Zbl0070.34602MR86986
- [6] T. Kato, Linear evolution equations of hyperbolic type. J. Fac. Sci. Univ. Tokyo, Sec. 1, t. 17, 1970, p. 241-258. Zbl0222.47011MR279626
- [7] T. Kato, Linear evolution equations of hyperbolic type. II. J. Math. Soc. Japan, t. 25, 1973, 648-666. Zbl0262.34048MR326483
- [8] M. Reed, B. Simon, Methods of modern mathematical physics. I. Functional analysis. New York, Academic Press, 1972. Zbl0242.46001MR493419
- [9] M. Reed, B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, New York, Academic Press, 1975. Zbl0308.47002MR493420
- [10] M. Reed, B. Simon, Methods of modern mathematical physics. IV. Analysis of operators, New York, Academic Press, 1978. Zbl0401.47001MR493421
- [11] B. Simon, Quantum Mechanicsfor Hamiltonians defined as Quadratic Forms, Princeton University Press, 1971. Zbl0232.47053MR455975
- [12] H. Tanabe, Equations of Evolution, Pitman, 1979. MR533824
- [13] U. Wüller, Existenz von Propagatoren für Schrödinger Operatoren mit zeitabhängigen singulären Potentialen, Diplomarbeit, Ruhr-UniversitätBochum, 1984.
- [14] K. Yajima, A multi-channel scattering theory for some time dependent hamiltonians, Charge transfer problem. Comm. Math. Phys., t. 75, 1980, p. 153-178. Zbl0437.47008MR582506
- [15] K. Yosida, On the integration of the equation of evolution. J. Fac. Sci. Univ. Tokyo, Sec. 1, t. 9, 1963, p. 397-402. Zbl0201.18203MR150616
- [16] K. Yosida, Time dependent evolution equations in a locally compact space. Math. Ann., t. 162, 1966, p. 83-86. Zbl0138.08301MR190498
- [17] K. Yosida, Functional Analysis, Berlin, Heidelberg, New York, Springer, 2nd. ed., 1968. Zbl0152.32102MR500055
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