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Volumn 43, Issue 1, 1991, Pages 44-56

Wigner function in Liouville space: A canonical formalism

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EID: 0002113773     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.43.44     Document Type: Article
Times cited : (86)

References (45)
  • 1
    • 84926789321 scopus 로고    scopus 로고
    • For reviews, see (a) S. R. de Groot and L. G. Suttorp, Foundations of Electrodynamics (North-Holland, Amsterdam, 1972), Appendix to Chap. VI;
  • 13
    • 84926811353 scopus 로고
    • The Liouville space bra-ket notation is found, e.g., in (a), in Proble`me a` N Corps, 1967 Les Houches Lectures, edited by C. De Witt and, (Gordon and Breach, London, 1968), and is used extensively in spectroscopy, where it was introduced by (b) A. Ben-Reuven
    • (1966) Phys. Rev. , vol.141 , pp. 34
    • des Cloiseaux, J.1    Balian, R.2
  • 20
    • 84926855264 scopus 로고    scopus 로고
    • H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1950), pp. 272 – 276.
  • 21
    • 84926811352 scopus 로고    scopus 로고
    • P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford University Press, New York, 1958), pp. 83 – 89.
  • 22
    • 84926855263 scopus 로고    scopus 로고
    • For example, Dirac [who denotes the position operator by q and positions (numbers) by q prime] lets | PSI (q) rangle be the ket whose projection on langle q prime | is PSI ( q prime ). Our partial / partial (q hat ) is denoted d / d q by Dirac.
  • 25
    • 84926855262 scopus 로고    scopus 로고
    • F. R. Gantmacher, The Theory of Matrices (Chelsea, New York, 1960), Vol. 1, Chap. VIII.
  • 26
    • 84926811351 scopus 로고    scopus 로고
    • Note that (6.5) alone, without Galilean invariance, does not necessarily imply (6.4) mdashone could have τ hat hat | u ; φ rcurl = ei γ | τ u ; φ rcurl where the phase gamma may depend on tau and u.
  • 27
    • 4244198097 scopus 로고
    • discussed this canonical set of superoperators, but without relating it to the Wigner-Weyl formulation.
    • (1979) Physica A , vol.99 , pp. 369
    • George, C.1    Prigogine, I.2
  • 34
    • 84926811350 scopus 로고    scopus 로고
    • R. P. Feynman, in Quantum Implications, Essays in Honour of David Bohm, edited by B. J. Hiley and F. D. Peat (Routledge and Kegan Paul, New York, 1987); see also Ref. 15.
  • 37
    • 84926855260 scopus 로고    scopus 로고
    • This may be seen by proceeding as in Eq. (2.15), using (7.1) instead of (2.6).
  • 38
    • 84926855259 scopus 로고    scopus 로고
    • F. Bopp, in Werner Heisenberg und die Physik unserer Zeit (Vieweg, Braunschweig, 1961), p. 128;
  • 40
    • 84926855258 scopus 로고    scopus 로고
    • (a) I. Prigogine, Non-Equilibrium Statistical Mechanics (Wiley, New York, 1962);
  • 43
    • 84926789319 scopus 로고    scopus 로고
    • (b) A. Royer, in The Physics of Phase Space, edited by Y. S. Kim and W. W. Zachary (Springer, New York, 1987);


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.