HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 21 (1959) > Number 4
| Next Article >

Prog. Theor. Phys. Vol. 21 No. 4 (1959) pp. 625-639

[ Full Text PDF : FREE ACCESS (935K) ]

On the Relation between the Phase Shift and the Number of Bound States

Masakuni Ida

Department of Physics, Kyoto University, Kyoto

(Received December 8, 1958)

Abstract:

Some features of the Low equation are studied for Dyson's model. To select a unique solution the relation between the phase shift and the number of bound states is important. (§1) This relation is investigated more generally. It is connected with the energy spectra of the free Hamiltonian. (§2) The relation between the phase shift and the number of resonant states is also shown. Resonances are classified into two types and some differences in their properties are stated. (§3)


URL : http://ptp.ipap.jp/link?PTP/21/625/
DOI : 10.1143/PTP.21.625

[ Full Text PDF : FREE ACCESS (935K) ] Citation:

References:

  1. F. E. Low, Phys. Rev. 97 (1955), 1392[APS].
  2. M. Gell-Mann, M. L. Goldberger and W. E. Thirring, Phys. Rev. 95 (1954), 1612[APS].
  3. H. Lehmann, K. Symanzik and W. Zimmermann, Nuovo Cim. 1 (1955), 205.
  4. L. Castillejo, R. H. Dalitz and F. J. Dyson, Phys. Rev. 101 (1956), 453[APS]. See also H. Fukutome, Prog. Theor. Phys. 17 (1957), 383[PTP].
  5. R. Haag, Nuovo Cim. 5 (1957), 203.
  6. N. Levinson, Kgl. Danske Vid. Selsk. Mat.-fys. Medd. 25 No. 9 (1949).
  7. F. J. Dyson, Phys. Rev. 106 (1957), 157[APS].
    See also R. E. Norton and A. Klein, Phys. Rev. 109 (1958), 991[APS].
  8. D. B. Fairlie and J. C. Polkinghorne, Nuovo Cim. 8 (1958), 345; ibid. 8 (1958), 555.
  9. J. M. Jauch, Helv. Phys. Acta 30 (1957), 143.
  10. A. Herglotz, Ber. Verhandl. Sachs. Ges. Wiss. Leipzig, Math-phys. 63 (1911), 501.
    J. A. Shohat and J. D. Tamarkin, The Problem of Moments (Am. Math. Soc., New York, 1943), Chap. II.
  11. H. Araki, Y. Munakata, M. Kawaguchi and T. Gotô, Prog. Theor. Phys. 17 (1957), 419[PTP].
    V. Glaser and G. Källèn, Nucl. Phys. 2 (1957), 706[CrossRef].
  12. F. Duimio, Nuovo Cim. 8 (1958), 826.
  13. T. D. Lee, Phys. Rev. 95 (1954), 1329[APS].
  14. G. Källèn and W. pauli, Kgl. Daneke Vid. Selsk. Mat.-fys. Medd. 30 No. 7 (1955).
  15. C. Møller, Kgl. Danske Vid. Selsk. Mat.-fys. Medd. 23 No. 1 (1945).
  16. As for Levinson's theorem in the scattering problem for non-local separable potentials,
    see M. Gourdin and A. Martin, Nuovo Cim. 6 (1957), 757;
    A. Martin, Nuovo Cim. 7 (1958), 607.
  17. S. T. Ma, Rev. Mod. Phys. 25 (1953), 853[APS].
  18. E. P. Wigner, Phys. Rev. 98 (1955), 145[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 22 No. 6 (1959) pp. 807-813 :
    On Levinson's Theorem in the Theory of Multi-Channel Scattering
    Gaku Konisi and Takesi Ogimoto
  2. Progress of Theoretical Physics Vol. 23 No. 2 (1960) pp. 376-378 :
    A Note on the Phenomenological Theory of Unstable Particles
    Andrzej Krzywicki and Jerzy Szymanski
  3. Progress of Theoretical Physics Vol. 25 No. 3 (1961) pp. 381-403 :
    Phase Shift and Identities in Quantized Field Theory
    Shûkô Azuma
  4. Progress of Theoretical Physics Vol. 25 No. 3 (1961) pp. 404-410 :
    Dispersion Relations and High Energy Limits in Quantum Field Theory. II
    Seiya Aramaki
  5. Progress of Theoretical Physics Vol. 25 No. 6 (1961) pp. 981-988 :
    Dispersion Relations and High Energy Limits in Quantum Field Theory. III
    Seiya Aramaki
  6. Progress of Theoretical Physics Vol. 25 No. 6 (1961) pp. 1028-1034 :
    The Σ-Λ Relative Parity and the K-N Reaction. II
    Yukihisa Nogami
  7. Progress of Theoretical Physics Vol. 26 No. 6 (1961) pp. 861-878 :
    Energy Spectrum and Determinant Method in Quantized Field Theory
    Shûkô Azuma
  8. Progress of Theoretical Physics Vol. 27 No. 1 (1962) pp. 33-50 :
    Pion-Pion Interaction
    Shin Ishida and Kazo Nakazawa
  9. Progress of Theoretical Physics Vol. 27 No. 5 (1962) pp. 849-881 :
    Effective Range Theory of Multichannel Reactions in the Chain Approximation Method
    Yasunori Fujii
  10. Progress of Theoretical Physics Vol. 29 No. 1 (1963) pp. 71-86 :
    A Classification of Resonances
    Yasunori Fujii
  11. Progress of Theoretical Physics Vol. 29 No. 1 (1963) pp. 87-96 :
    Use of the Generalized Jost Function in Quantum Field Theory
    Takeshi Kanki
  12. Progress of Theoretical Physics Vol. 29 No. 1 (1963) pp. 97-103 :
    Restriction on the Coupling Constant from Analyticity and Unitarity of the S-Matrix
    Takeshi Kanki and Takesi Ogimoto
  13. Progress of Theoretical Physics Vol. 29 No. 1 (1963) pp. 104-127 :
    Towards Unified and Convergent Theory of Elementary Particles
    Sho Tanaka
  14. Progress of Theoretical Physics Vol. 34 No. 1 (1965) pp. 92-115 :
    Green's Funtion Approach and Its Equivalence with the Ordinary N/D Method
    Masakuni Ida
  15. Progress of Theoretical Physics Vol. 34 No. 3 (1965) pp. 455-461 :
    Range of Validity of the One-Boson-Exchange Model
    Yogiro Hama and Norio Hoshizaki
  16. Progress of Theoretical Physics Vol. 35 No. 1 (1966) pp. 104-116 :
    A General Effective-Range Formula and the Compositeness of the Deuteron
    Masakuni Ida
  17. Progress of Theoretical Physics Vol. 35 No. 3 (1966) pp. 452-462 :
    Vertex Zeros and Levinson's Theorem
    Koichi Hayashi
  18. Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1344-1356 :
    A Phase-Shift Analysis of Proton-Proton Scattering at PL=6 GeV/c
    Masanori Matsuda, Hiroshi Suemitsu, Wataro Watari and Minoru Yonezawa

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.