Structure of the scattering operator for time-periodic Schrödinger equations

Shu NAKAMURA

doi:10.2969/jmsj/03820261

Shu NAKAMURA

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 2 Pages 261-273

DOI https://doi.org/10.2969/jmsj/03820261

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Published: 1986 Received: October 31, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) E. B. Davies, Time-dependent scattering theory, Math. Ann., 210 (1974), 149-162.
2) V. Enss, Asymptotic completeness for quantum mechanical potential scattering, Commun. Math. Phys., 61 (1978), 285-291.
3) V. Enss and K. Veselic, Bound states and propagating states for time-dependent Hamiltonians, Ann. Inst. H. Poincaré, 39 (1983), 159-191.
4) J. Ginibre and M. Moulin, Hilbert space approach to the quantum mechanical three-body problem, Ann. Inst. H. Poincaré, 21 (1974), 97-145.
5) J. S. Howland, Stationary scattering theory for time-dependent Hamiltonian, Math. Ann., 207 (1974), 315-335.
6) J. S. Howland, Scattering theory for Hamiltonians periodic in time, Indiana Univ. Math. J., 28(1979), 471-494.
7) T. Kato, Linear evolution equations of “hyperbolic” type II, J. Math. Soc. Japan, 25 (1973), 648-666.
8) H. Kitada and K. Yajima, A scattering theory for time-dependent long-range potentials, Duke Math. J., 49(1983), 341-376.
9) S. T. Kuroda, Scattering theory for differential operators I, Operator theory, J. Math. Soc. Japan., 25(1973), 75-104.
10) S. T. Kuroda, An Introduction to Scattering Theory, Lecture Note Series, No. 51, Aarhas Univ., 1978.
11) S. Nakamura, On scattering theory for time-periodic quantum mechanical systems, Master thesis, Univ. of Tokyo, 1984 (in Japanese).
12) M. Reed and B. Simon, Methods of Modern Mathematical Physics I-IV, Academic Press, New York, 1972-1979.
13) E. J. P. G. Schmidt, On scattering by time-dependent perturbations, Indiana Univ. Math. J., 24 (1975), 925-935.
14) K. Yajima, Scattering theory for Schrödinger equations with potentials periodic in time, J. Math. Soc. Japan, 29(1977), 729-743.
15) K. Yajima, Large time behavior of time-periodic quantum systems, Differential Equations, Proc. Int. Conf. Birmingham, Math. Studies, 92, North-Holland, 1984.
16) K. Yajima and H. Kitada, Bound states and scattering states for time periodic Hamiltonians, Ann. Inst. H. Poincaré, 39(1983), 145-157.

Right : [1] E. B. Davies, Time-dependent scattering theory, Math. Ann., 210 (1974), 149-162.
[2] V. Enss, Asymptotic completeness for quantum mechanical potential scattering, Commun. Math. Phys., 61 (1978), 285-291.
[3] V. Enss and K. Veselic, Bound states and propagating states for time-dependent Hamiltonians, Ann. Inst. H. Poincaré, 39 (1983), 159-191.
[4] J. Ginibre and M. Moulin, Hilbert space approach to the quantum mechanical three-body problem, Ann. Inst. H. Poincaré, 21 (1974), 97-145.
[5] J. S. Howland, Stationary scattering theory for time-dependent Hamiltonian, Math. Ann., 207 (1974), 315-335.
[6] J. S. Howland, Scattering theory for Hamiltonians periodic in time, Indiana Univ. Math. J., 28(1979), 471-494.
[7] T. Kato, Linear evolution equations of “hyperbolic” type II, J. Math. Soc. Japan, 25 (1973), 648-666.
[8] H. Kitada and K. Yajima, A scattering theory for time-dependent long-range potentials, Duke Math. J., 49(1983), 341-376.
[9] S. T. Kuroda, Scattering theory for differential operators I, Operator theory, J. Math. Soc. Japan., 25(1973), 75-104.
[10] S. T. Kuroda, An Introduction to Scattering Theory, Lecture Note Series, No. 51, Aarhas Univ., 1978.
[11] S. Nakamura, On scattering theory for time-periodic quantum mechanical systems, Master thesis, Univ. of Tokyo, 1984 (in Japanese).
[12] M. Reed and B. Simon, Methods of Modern Mathematical Physics I-IV, Academic Press, New York, 1972-1979.
[13] E. J. P. G. Schmidt, On scattering by time-dependent perturbations, Indiana Univ. Math. J., 24 (1975), 925-935.
[14] K. Yajima, Scattering theory for Schrödinger equations with potentials periodic in time, J. Math. Soc. Japan, 29(1977), 729-743.
[15] K. Yajima, Large time behavior of time-periodic quantum systems, Differential Equations, Proc. Int. Conf. Birmingham, Math. Studies, 92, North-Holland, 1984.
[16] K. Yajima and H. Kitada, Bound states and scattering states for time periodic Hamiltonians, Ann. Inst. H. Poincaré, 39(1983), 145-157.

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