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Prog. Theor. Phys. Vol. 7 No. 2 (1952) pp. 171-184

[ Full Text PDF : FREE ACCESS (1063K) ]

On the Analytic Behaviour of Dyson Transformation Function

Hiroshi Suura, Yoichi Mimura and Toshiei Kimura*

Department of Physics, Hiroshima University
*Institute for Theoretical Physics, Hiroshima University

(Received December 17, 1951)

Abstract:

The detailed properties of the Dyson transformation function, which represents the time development of an initial free state at infinite past due to an interaction, adiabatically switched in and off according to a factor exp (-ε|t|\hbar), (ε > 0), were examined in special connection with bound states. The transformation function is unitary and the power expansion in the interaction Hamiltonian is finite and regular in the limit ε → 0, except those matrix elements with respect to the lowest energy free state of the system in question. An initial free state except the lowest energy one is transformed at a finite time t into the corresponding unbound eigenstate of the total Hamiltonian with the same energy. Transitions to bound states are due to those initial states whose energy falls in the interval of the order ε from that of the lowest energy state.


URL : http://ptp.ipap.jp/link?PTP/7/171/
DOI : 10.1143/PTP.7.171

[ Full Text PDF : FREE ACCESS (1063K) ] Citation:

References:

  1. B. Ferretti, Nuovo Cim. 8 (1951), 108.
    H. S. Snyder, Phys. Rev. 83 (1951), 1154[APS].
    M. Gell-Mann and F. Low, Phys. Rev. 84 (1951), 350[APS].
  2. C. Møller, Kgl. Danske Vidensk. Selsk. Math. -fys. Medd. 23 (1945), Nr. 1; ibid. 24 (1946), Nr. 19.
  3. B. A. Lippmann and J. Schwinger, Phys. Rev. 79 (1950), 469[APS].
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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 13 No. 5 (1955) pp. 497-504 :
    Adiabatic Process and the Stationary State
    Hajime Tanaka
  2. Progress of Theoretical Physics Vol. 14 No. 3 (1955) pp. 175-197 :
    The Formal Theory of Scattering
    Sigenobu Sunakawa
  3. Progress of Theoretical Physics Vol. 18 No. 1 (1957) pp. 51-65 :
    Criticism on the Assumptions in the Formal Scattering Theory
    Tsutomu Imamura
  4. Progress of Theoretical Physics Vol. 18 No. 6 (1957) pp. 559-566 :
    A New Approach to a Bound State
    Tsutomu Imamura

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