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Progress of Theoretical Physics

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

Toshiharu Kawai

Published May 1, 1973• 5 citations
Publisher

Abstract

Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 680–690 Schwinger’s Variational Principle in Quantum Mechanics with Velocity Dependent Potential. III Hideki Kamo and Toshiharu Kawai 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

DOI
10.1143/ptp.49.1777

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Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 680–690 Schwinger’s Variational Principle in Quantum Mechanics with Velocity Dependent Potential. III Hideki Kamo and Toshiharu Kawai 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
Progress of Theoretical Physics Vol. 29 No. 2 (1963) pp. 296-320 Quantization of the Gravitational Field in the Expanding Universe Hidekazu Nariai and Toshiei Kimura Progress of Theoretical Physics Vol. 93 No. 5 (1995) pp. 949-960 Systematic Treatment of General Time-Dependent Harmonic Oscillator in Classical and Quantum Mechanics Hirotaka Kanasugi and Hidehiko Okada Progress of Theoretical Physics Vol. 98 No. 2 (1997) pp. 321-329 A Fresh Look at the BCK Frictional Lagrangian Vairelil J. Menon, Namrata Chanana and Yashwant Singh Progress of Theoretical Physics Vol. 125 No. 6 (2011) pp. 1133-1141 Quantum Description of a Mesoscopic RLC Circuit I. A. Pedrosa and A. P. Pinheiro
Progress of Theoretical Physics Vol. 29 No. 2 (1963) pp. 296-320 Quantization of the Gravitational Field in the Expanding Universe Hidekazu Nariai and Toshiei Kimura Progress of Theoretical Physics Vol. 93 No. 5 (1995) pp. 949-960 Systematic Treatment of General Time-Dependent Harmonic Oscillator in Classical and Quantum Mechanics Hirotaka Kanasugi and Hidehiko Okada Progress of Theoretical Physics Vol. 98 No. 2 (1997) pp. 321-329 A Fresh Look at the BCK Frictional Lagrangian Vairelil J. Menon, Namrata Chanana and Yashwant Singh Progress of Theoretical Physics Vol. 125 No. 6 (2011) pp. 1133-1141 Quantum Description of a Mesoscopic RLC Circuit I. A. Pedrosa and A. P. Pinheiro
Progress of Theoretical Physics Vol. 8 No. 6 (1952) pp. 655-668 A Quantum Theory of Boson Assemblies, I Toshiyuki Nishiyama Progress of Theoretical Physics Vol. 27 No. 3 (1962) pp. 600-607 Collective Description of a System of Interacting Bose Particles. II Sigenobu Sunakawa, Hiroshi Nakatani and Yoshimatsu Yoko-o Progress of Theoretical Physics Vol. 52 No. 6 (1974) pp. 1784-1797 A Long-Range Attractive Interaction of Rotons in Superfluid 4He Toshiyuki Nishiyama and Shunkichi Sai Progress of Theoretical Physics Vol. 53 No. 2 (1975) pp. 386-399 On the Validity of Collective Variable Description of Bose Systems Minoru Takahashi Progress of Theoretical Physics Vol. 53 No. 5 (1975) pp. 1243-1266 On the Collective Variables in Many-Boson System Shuichiro Yamasaki, Takeji Kebukawa and Sigenobu Sunakawa Progress of Theoretical Physics Vol. 54 No. 2 (1975) pp. 384-395 Ground-State Energy of a Many-Boson System Toshiyuki Nishiyama Progress of Theoretical Physics Vol. 54 No. 2 (1975) pp. 597-599 Momentum Distribution of an Interacting Many-Boson System Toshiyuki Nishiyama Progress of Theoretical Physics Vol. 56 No. 2 (1976) pp. 375-395 A Microscopic Theory of the Interacting Bose System Shosuke Sasaki and Kiyohisa Matsuda Progress of Theoretical Physics Vol. 57 No. 2 (1977) pp. 393-409 Collective Variable Approach to Many-Boson Systems at High Density Toshiyuki Nishiyama and Masakazu Tsujii Progress of Theoretical Physics Vol. 62 No. 6 (1979) pp. 1487-1498 Generalized Solutions to the Gross-Pitaevskii Equation Masakazu Ichiyanagi Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1248-1264 Bose-Einstein Condensation and the Canonical Conjugates to the Density Fluctuations Shuichiro Yamasaki and Masahiko Hirooka Progress of Theoretical Physics Vol. 64 No. 5 (1980) pp. 1565-1576 Momentum Distribution and Ground-State Energy of Liquid 4He at the Absolute Zero Temperature Toshiyuki Nishiyama and Yoiti Watanabe Progress of Theoretical Physics Vol. 67 No. 3 (1982) pp. 726-742 On the Hydrodynamical Model for a Bose Liquid at T=0 Masakazu Ichiyanagi and Masato Ohya Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1482-1503 Quasi-Particle Description of a Degenerate System of Bosons Masahiko Hirooka and Shuichiro Yamasaki
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.
Progress of Theoretical Physics Vol. 10 No. 1 (1953) pp. 121-122 Equivalence between the Formulation of Quantum Mechanics in terms of Quantum Potential and the One in terms of Markoff-like Process Takehiko Takabayasi Progress of Theoretical Physics Vol. 10 No. 1 (1953) pp. 122-124 Subsidiary Conditions in the Phase-space Representation of Quantum Mechanics Takehiko Takabayasi Progress of Theoretical Physics Vol. 11 No. 4 (1954) pp. 341-373 The Formulation of Quantum Mechanics in terms of Ensemble in Phase Space Takehiko Takabayasi