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The formulation of quantum mechanics in terms of phase space functions

Published online by Cambridge University Press:  24 October 2008

D. B. Fairlie
D. B. Fairlie
Affiliation:
St Salvator's College, St Andrews
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Abstract

A relationship between the Hamiltonian of a system and its distribution function in phase space is sought which will guarantee that the average energy is the weighted mean of the Hamiltonian over phase space. This relationship is shown to imply the existence of a wave function satisfying the Schrödinger equation, and dictates the possible forms of time-dependence of the distribution function.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 581 - 586
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1) Baker, G. A. Phys. Rev. 109 (1958), 2198–2206.CrossRefGoogle Scholar
(2) Bartlett, M. S. and Moyal, J. E. Proc. Cambridge Philos. Soc. 45 (1949), 545–553.CrossRefGoogle Scholar
(3) Brouwer, L. E. J. Math. Ann. 72 (1912), 34–57.Google Scholar
(4) Groenewold, H. J. Physica, 12 (1946), 405–460.CrossRefGoogle Scholar
(5) Moyal, J. E. Proc. Cambridge Philos. Soc. 45 (1949), 99–124.CrossRefGoogle Scholar
(6) Takabayasi, T. Progr. Theoret. Phys. 11 (1954), 341–373.CrossRefGoogle Scholar
(7) Wigner, E. P. Phya. Rev. 40 (1932), 749–759.CrossRefGoogle Scholar