Quick Search:
Author: Title/Abstract: Vol./No: Page:

Prog. Theor. Phys. Vol. 56 No. 3 (1976) pp. 919-925

[ Full Text PDF : FREE ACCESS (449K) ]

Asymptotic Behavior of the Eigenvalues in the Wick-Cutkosky Model for Large Principal Quantum Number

Noriaki Setô

Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606

(Received March 8, 1976)

Abstract:

The Wick-Cutkosky eigenvalue problem for the bound state in the Bethe-Salpeter equation is transformed into an operator form. With the aid of the representation thus obtained, the asymptotic behavior of the eigenvalues is found for large principal quantum number.


URL : http://ptp.ipap.jp/link?PTP/56/919/
DOI : 10.1143/PTP.56.919

[ Full Text PDF : FREE ACCESS (449K) ] Citation:


References:

  1. G. C. Wick, Phys. Rev. 96 (1954), 1124[APS].
  2. R. E. Cutkosky, Phys. Rev. 96 (1954), 1135[APS].
  3. Y. Nambu, Prog. Theor. Phys. 5 (1950), 614[PTP].
    E. E. Salpeter and H. A. Bethe, Phys. Rev. 84 (1951), 1232[APS].
  4. For a review, see Nakanishi's excellent paper;
    N. Nakanishi, Prog. Theor. Phys. Suppl. No. 43 (1961), 1[PTP].
  5. N. Nakanishi, Phys. Rev. 138 (1965), B1182[APS].
  6. E. Kyriakopoulos, Phys. Rev. 174 (1968), 1846[APS].
  7. F. Tanaka and N. Nakanishi, Prog. Theor. Phys. 53 (1975), 797[PTP].
  8. E. zur Linden, Nuovo Cim. A 63 (1969), 181; ibid. 63 (1969), 193.
  9. N. Nakanishi, Phys. Rev. 136 (1964), B1830[APS].
  10. K. Seto, Prog. Theor. Phys. 40 (1968), 605[PTP].
  11. H. J. W. Müller, Z. Phys. 230 (1970), 89.
  12. R. Gatto and P. Menotti, Nuovo Cim. A 68 (1970), 118.
  13. N. Murai, K. Nakamura and H. Ezawa, Prog. Theor. Phys. 46 (1971), 909[PTP].
  14. F. T. Hadjioannou and E. Kyriakopoulos, Int. J. Theor. Phys. 5 (1972), 199.
  15. A. Erdélyi, Higher Transcendental Functions Vol. I. (McGraw-Hill, New York, 1953), p. 178.
  16. N. Ja. Vilenkin, Special Functions and the Theory of Group Representations (Amer. Math. Soc. Providence, 1968), p. 561.
  17. C. M. Bender and T. T. Wu, Phys. Rev. 184 (1969), 1231[APS].
  18. J. J. Loeffel, A. Martin, B. Simon and A. S. Wightman, Phys. Lett. B 30 (1969), 656[CrossRef].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 57 No. 4 (1977) pp. 1403-1408 :
    Reflection Symmetry of the Eigenvalues in the Wick-Cutkosky Model
    Noriaki Setô
  2. Progress of Theoretical Physics Supplement No.95 (1988) pp. 1-24 :
    Review of the Wick-Cutkosky Model
    Noboru Nakanishi