Scattering theory for Schrödinger equations with potentials periodic in time

Kenji YAJIMA

doi:10.2969/jmsj/02940729

Kenji YAJIMA

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JOURNAL FREE ACCESS

1977 Volume 29 Issue 4 Pages 729-743

DOI https://doi.org/10.2969/jmsj/02940729

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Published: 1977 Received: July 02, 1976 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) S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Annali dela Scuola Normale Pisa, Ser. IV, 2.2 (1975), 151-218.
2) V.S. Buslaev and V.B. Matveev, Wave operators for Schrödinger equation with slowly decreasing potential, Theoret. and Math. Phys., 2 (1970), 266-274 (English translation from Russian).
3) M.N. Cook, On convergence to the Møller wave matrix, J. Math. and Phys., 36 (1957), 82-87.
4) E.B. Davies, Time dependent scattering theory, Math. Ann., 210 (1974), 149-162.
5) J.D. Dollard, Asymptotic convergence and the Coulomb interaction, J. Math. Phys., 5 (1964), 729-738.
6) M.N. Hack, On the convergence to the Møller wave operators, Nuovo Cimento, 13 (1959), 231-236.
7) J. Howland, Stationary scattering theory for time dependent Hamiltonians, Math. Ann., 207 (1974), 315-335.
8) A. Inoue, Wave and scattering operators for an evolution system (d/dt)+iA(t), J. Math. Soc. Japan, 26 (1974), 608-624.
9) T. Kako and K. Yajima, Spectral and scattering theory for a class of non-selfadjoint operators, to appear.
10) T. Kato, Perturbation theory for linear operators, Springer Verlag, Berlin-Heidelberg-New York, 1966.
11) T. Kato, Wave operators and similarity for some nonselfadjoint operators, Math. Ann., 162 (1966), 258-276.
12) T. Kato, Linear evolution equations of “hyperbolic” type, J. Fac. Sci. Univ. Tokyo, Sect. IA, 17 (1970), 241-258.
13) T. Kato, Linear evolution equations of “hyperbolic” type II, J. Math. Soc. Japan, 25 (1973), 648-666.
14) T. Kato and S.T. Kuroda, The abstract theory of scattering, Rocky Mountain J. Math., 1 (1971), 127-171.
15) J. Kisynski, Sur les opérateurs de Green des problémes de Cauchy abstraits, Studia Math., 23 (1964), 285-328.
16) S.T. Kuroda, An abstract stationary approach to perturbation of continuous spectra and scattering theory, J. Analyse Math., 20 (1967), 57-117.
17) S.T. Kuroda, Scattering theory for differential operators, I, Operator theory, J. Math. Soc. Japan., 25 (1973), 75-104.
18) S.T. Kuroda and H. Morita, to appear.
19) G. Schmidt, On scattering by time dependent perturbations, India Univ. Math. J., 24 (1975), 925-935.
20) B. Simon, Quantum mechanics for Hamiltonians defined as quadratic forms, Princeton Univ. Press, 1971.

Right : [1] S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Annali dela Scuola Normale Pisa, Ser. IV, 2.2 (1975), 151-218.
[2] V. S. Buslaev and V. B. Matveev, Wave operators for Schrödinger equation with slowly decreasing potential, Theoret. and Math. Phys., 2 (1970), 266-274 (English translation from Russian).
[3] M. N. Cook, On convergence to the Møller wave matrix, J. Math. and Phys., 36 (1957), 82-87.
[4] E. B. Davies, Time dependent scattering theory, Math. Ann., 210 (1974), 149-162.
[5] J. D. Dollard, Asymptotic convergence and the Coulomb interaction, J. Math. Phys., 5 (1964), 729-738.
[6] M. N. Hack, On the convergence to the Møller wave operators, Nuovo Cimento, 13 (1959), 231-236.
[7] J. Howland, Stationary scattering theory for time dependent Hamiltonians, Math. Ann., 207 (1974), 315-335.
[8] A. Inoue, Wave and scattering operators for an evolution system (d/dt)+iA(t), J. Math. Soc. Japan, 26 (1974), 608-624.
[9] T. Kako and K. Yajima, Spectral and scattering theory for a class of non-selfadjoint operators, to appear.
[10] T. Kato, Perturbation theory for linear operators, Springer Verlag, Berlin-Heidelberg-New York, 1966.
[11] T. Kato, Wave operators and similarity for some nonselfadjoint operators, Math. Ann., 162 (1966), 258-276.
[12] T. Kato, Linear evolution equations of “hyperbolic” type, J. Fac. Sci. Univ. Tokyo, Sect. IA, 17 (1970), 241-258.
[13] T. Kato, Linear evolution equations of “hyperbolic” type II, J. Math. Soc. Japan, 25 (1973), 648-666.
[14] T. Kato and S. T. Kuroda, The abstract theory of scattering, Rocky Mountain J. Math., 1 (1971), 127-171.
[15] J. Kisynski, Sur les opérateurs de Green des problémes de Cauchy abstraits, Studia Math., 23 (1964), 285-328.
[16] S. T. Kuroda, An abstract stationary approach to perturbation of continuous spectra and scattering theory, J. Analyse Math., 20 (1967), 57-117.
[17] S. T. Kuroda, Scattering theory for differential operators, I, Operator theory, J. Math. Soc. Japan., 25 (1973), 75-104.
[18] S. T. Kuroda and H. Morita, to appear.
[19] G. Schmidt, On scattering by time dependent perturbations, India Univ. Math. J., 24 (1975), 925-935.
[20] B. Simon, Quantum mechanics for Hamiltonians defined as quadratic forms, Princeton Univ. Press, 1971.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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