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Prog. Theor. Phys. Vol. 50 No. 2 (1973) pp. 680-690

[ Full Text PDF : FREE ACCESS (708K) ]

Schwinger's Variational Principle in Quantum Mechanics with Velocity Dependent Potential. III

Hideki Kamo and Toshiharu Kawai

Department of Physics, Osaka City University, Osaka

(Received February 21, 1973)

Abstract:

Schwinger's variational principle is formulated for the multi-dimensional quantum system which corresponds to the classical system described by the Lagrangian Lc(\dotx,x)=(M/2)gij(x)\dotxi\dotxj-v(x). The c-number variations of coordinates and time are sufficient to give the laws of quantum mechanics. The Euler-Lagrange equation, the canonical equations of motion and the canonical commutation relations are derived from this principle and there is no inconsistency. An appropriate choice of the Lagrangian operator is essential in our formulation. It is shown that an arbitrary point transformation is entitled to be called a canonical transformation. Ambiguities in the quantal Lagrangian are also discussed.


URL : http://ptp.ipap.jp/link?PTP/50/680/
DOI : 10.1143/PTP.50.680

[ Full Text PDF : FREE ACCESS (708K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 50 No. 5 (1973) pp. 1715-1728 :
    Q-Number Variational Method for Non-Linear Lagrangian in Quantum Mechanics
    Teruya Ohtani and Reiji Sugano
  2. Progress of Theoretical Physics Vol. 50 No. 5 (1973) pp. 1769-1771 :
    Note on Quantum Form of Non-Linear Lagrangian
    Toshiei Kimura
  3. Progress of Theoretical Physics Vol. 52 No. 5 (1974) pp. 1687-1701 :
    A Quantum-Theoretical Lagrangian Formalism for Quasi-Linear Field Theories. I
    Takao Okabayashi and Hiroyuki Kikugawa
  4. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1964-1972 :
    On the Path Integral in the Curved Space
    Toshiei Kimura
  5. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1827-1842 :
    Quantum Theory of Massive Yang-Mills Fields. I
    Takashi Fukuda, Minoru Monda, Minoru Takeda and Kan-ichi Yokoyama

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