Spectral analysis for N-particle systems with Stark effect non-existence of bound states and principle of limiting absorption

Hideo TAMURA

doi:10.2969/jmsj/04630427

Spectral analysis for N-particle systems with Stark effect

non-existence of bound states and principle of limiting absorption

Hideo TAMURA

著者情報

ジャーナルフリー

1994 年 46 巻 3 号 p. 427-448

DOI https://doi.org/10.2969/jmsj/04630427

詳細

Published: 1994 Received: 1992/12/24 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : Spectral analysis for N-particle systems with Stark effect: non-existence of bound states and principle of limiting absorption
Right : Spectral analysis for N-particle systems with Stark effect

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Right : non-existence of bound states and principle of limiting absorption

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. E. Avron and I. W. Herbst, Spectral and scattering theory of Schrödinger operators related to the Stark effect, Comm. Math. Phys., 52 (1977), 239-254.
2) H. Cycon, R. G. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Springer, 1988.
3) R. G. Froese and I. W. Herbst, Exponential bounds and absence of positive eigenvalues of N-body Schrödinger operators, Comm. Math. Phys., 87 (1982), 429-447.
4) G. M. Graf, Asymptotic completeness for N-body short-range quantum systems: a new proof, Comm. Math. Phys., 132 (1990), 73-101.
5) I. W. Herbst, Unitary equivalence of Stark effect Hamiltonians, Math. Z., 155 (1977), 55-79.
6) A. Jensen, Asymptotic completeness for a new class of Stark effect Hamiltonians, Comm. Math. Phys., 107 (1986), 21-28.
7) A. Jensen and K. Yajima, On the long range scattering for Stark Hamiltonians, J. Reine Angew. Math., 420 (1991), 179-193.
8) T. Kato, Wave operators and similarity for some nonselfadjoint operators, Math. Ann., 162 (1966), 258-278.
9) H. Kitada, Asymptotic completeness of N-body wave operators I. Short-range quantum systems, Rev, in Math. Phys., 3 (1991), 101-124.
10) E. L. Korotyaev, On the scattering theory of several particles in an external electric fields, Math. USSR-Sb., 60 (1988), 177-196.
11) E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys., 78 (1981), 391-408.
12) P. Perry, Scattering Theory by the Enss Method, Math. Rep., Vol. 1, Harwood Academic, 1983.
13) P. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. of Math., 114 (1981), 517-567.
14) M. Reed and B. Simon, Methods of Modern Mathematical Physics III, Scattering Theory, Academic Press, 1978.
15) I. M. Sigal, Stark effect in multielectron systems: non-existence of bound states, Comm. Math. Phys., 122 (1989), 1-22.
16) I. M. Sigal and A. Soffer, The N-particle scattering problem: asymptotic completeness for short-range systems, Ann. of Math., 125 (1987), 35-108.
17) H. Tamura, Asymptotic completeness for N-body Schrödinger operators with short-range interactions, Comm. Partial Differential Equations, 16 (1991), 1129-1154.
18) H. Tamura, Spectral and scattering theory for 3-particle Hamiltonian with Stark effect: asymptotic completeness, Osaka J. Math., 29 (1992), 135-159.
19) E. C. Titchmarsh, Eigenfunction Expansions Associated with Second Order Differential Equations, Oxford University Press, 1958.
20) D. White, The Stark effect and long range scattering in two Hilbert spaces, Indiana Univ. Math. J., 39 (1990), 517-546.
21) D. Yafaev, Radiation conditions and scattering theory for N-particle Hamiltonians, Comm. Math. Phys., 154 (1993), 523-554.
22) K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark-effect, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 377-390.

Right : [1] J. E. Avron and I. W. Herbst, Spectral and scattering theory of Schrödinger operators related to the Stark effect, Comm. Math. Phys., 52 (1977), 239-254.
[2] H. Cycon, R. G. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Springer, 1988.
[3] R. G. Froese and I. W. Herbst, Exponential bounds and absence of positive eigenvalues of N-body Schrödinger operators, Comm. Math. Phys., 87 (1982), 429-447.
[4] G. M. Graf, Asymptotic completeness for N-body short-range quantum systems: a new proof, Comm. Math. Phys., 132 (1990), 73-101.
[5] I. W. Herbst, Unitary equivalence of Stark effect Hamiltonians, Math. Z., 155 (1977), 55-79.
[6] A. Jensen, Asymptotic completeness for a new class of Stark effect Hamiltonians, Comm. Math. Phys., 107 (1986), 21-28.
[7] A. Jensen and K. Yajima, On the long range scattering for Stark Hamiltonians, J. Reine Angew. Math., 420 (1991), 179-193.
[8] T. Kato, Wave operators and similarity for some nonselfadjoint operators, Math. Ann., 162 (1966), 258-278.
[9] H. Kitada, Asymptotic completeness of N-body wave operators I. Short-range quantum systems, Rev, in Math. Phys., 3 (1991), 101-124.
[10] E. L. Korotyaev, On the scattering theory of several particles in an external electric fields, Math. USSR-Sb., 60 (1988), 177-196.
[11] E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys., 78 (1981), 391-408.
[12] P. Perry, Scattering Theory by the Enss Method, Math. Rep., Vol. 1, Harwood Academic, 1983.
[13] P. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. of Math., 114 (1981), 517-567.
[14] M. Reed and B. Simon, Methods of Modern Mathematical Physics III, Scattering Theory, Academic Press, 1978.
[15] I. M. Sigal, Stark effect in multielectron systems: non-existence of bound states, Comm. Math. Phys., 122 (1989), 1-22.
[16] I. M. Sigal and A. Soffer, The N-particle scattering problem: asymptotic completeness for short-range systems, Ann. of Math., 125 (1987), 35-108.
[17] H. Tamura, Asymptotic completeness for N-body Schrödinger operators with short-range interactions, Comm. Partial Differential Equations, 16 (1991), 1129-1154.
[18] H. Tamura, Spectral and scattering theory for 3-particle Hamiltonian with Stark effect: asymptotic completeness, Osaka J. Math., 29 (1992), 135-159.
[19] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second Order Differential Equations, Oxford University Press, 1958.
[20] D. White, The Stark effect and long range scattering in two Hilbert spaces, Indiana Univ. Math. J., 39 (1990), 517-546.
[21] D. Yafaev, Radiation conditions and scattering theory for N-particle Hamiltonians, Comm. Math. Phys., 154 (1993), 523-554.
[22] K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark-effect, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 377-390.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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