Wigner Method in Quantum Statistical Mechanics
dc.contributor.author | İmre, Kaya | en_US |
dc.contributor.author | Özizmir, Ercüment | en_US |
dc.contributor.author | Rosenbaum, Marcos | en_US |
dc.contributor.author | Zweifel, Paul Frederick | en_US |
dc.date.accessioned | 2010-05-06T23:14:24Z | |
dc.date.available | 2010-05-06T23:14:24Z | |
dc.date.issued | 1967-05 | en_US |
dc.identifier.citation | İmre, Kaya; Özizmir, Ercüment; Rosenbaum, Marcos; Zweifel, P. F. (1967). "Wigner Method in Quantum Statistical Mechanics." Journal of Mathematical Physics 8(5): 1097-1108. <http://hdl.handle.net/2027.42/71122> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/71122 | |
dc.description.abstract | The Wigner method of transforming quantum‐mechanical operators into their phase‐space analogs is reviewed with applications to scattering theory, as well as to descriptions of the equilibrium and dynamical states of many‐particle systems. Inclusion of exchange effects is discussed. | en_US |
dc.format.extent | 3102 bytes | |
dc.format.extent | 766628 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Wigner Method in Quantum Statistical Mechanics | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Nuclear Engineering, The University of Michigan, Ann Arbor, Michigan | en_US |
dc.contributor.affiliationum | Department of Nuclear Engineering, The University of Michigan, Ann Arbor, Michigan | en_US |
dc.contributor.affiliationother | Çekmece Nuclear Research and Training Center, Istanbul, Turkey | en_US |
dc.contributor.affiliationother | Department of Theoretical Physics, Middle East Technical University, Ankara, Turkey | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/71122/2/JMAPAQ-8-5-1097-1.pdf | |
dc.identifier.doi | 10.1063/1.1705323 | en_US |
dc.identifier.source | Journal of Mathematical Physics | en_US |
dc.identifier.citedreference | J. von Neumann, Mathematical Foundation of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1955). | en_US |
dc.identifier.citedreference | E. Wigner, Phys. Rev. 40, 749 (1932). | en_US |
dc.identifier.citedreference | There are several papers published which deal with the Wigner distribution function. Some of the basic references are: H. J. Groenewold, Physica 12, 405 (1946); J. E. Moyal, Proc. Cambridge Phil. Soc. 45, 99 (1949); J. H. Irving and R. W. Zwanzig, J. Chem. Phys. 19, 1173 (1951); H. Mori, I. Oppenheim, and J. Ross, in Studies in Statistical Mechanics, J. de Boer and G. E. Uhlenbeck, Eds. (North‐Holland Publishing Company, Amsterdam, 1962), Vol. 1. | en_US |
dc.identifier.citedreference | In our notation, r, p represent 3N‐dimensional vector c numbers for position and momentum variables and R, P represent the corresponding vector operators. A 3N‐dimensional scalar product is written as R.P or r.p. Also, Ri,Ri, PiPi: ri,ri, pi,pi, etc. denote ordinary three‐dimensional vectors associated with the ith particle. | en_US |
dc.identifier.citedreference | H. Weyl, The Theory of Groups and Quantum Mechanics (Dover Publications, New York, 1950). | en_US |
dc.identifier.citedreference | H. J. Groenewold, Ref. 3; several properties of the Wigner method have been first given in this work. | en_US |
dc.identifier.citedreference | This approach has been used by I. Oppenheim and J. Ross, Phys. Rev. 107, 28 (1957). | en_US |
dc.identifier.citedreference | L. Van Hove, Phys. Rev. 95, 249 (1954). | en_US |
dc.identifier.citedreference | E. Fermi, Ric. Sci. 7, 13 (1938); G. C. Summerfield, Ann. Phys. (N.Y.) 26, 72 (1964). | en_US |
dc.identifier.citedreference | B. N. Brockhouse in Proceedings of the Symposium on Inelastic Scattering of Neutrons in Solids and Liquids (International Atomic Energy Commission, Vienna, 1960). | en_US |
dc.identifier.citedreference | R. Nossal, Phys. Rev. 135, A1579 (1964). | en_US |
dc.identifier.citedreference | R. Aamodt, K. M. Case, M. Rosenbaum, and P. F. Zweifel, Phys. Rev. 126, 1165 (1962). | en_US |
dc.identifier.citedreference | Higher‐order corrections are studied in a paper by M. Rosenbaum and P. F. Zweifel, Phys. Rev. 137, B271 (1965); Also see M. Rosenbaum, Doctoral Thesis, University of Michigan (1964). | en_US |
dc.identifier.citedreference | For a general review, see W. E. Brittin and W. R. Chappell, Rev. Mod. Phys. 34, 620 (1962); also R. Balescu, Statistical Mechanics of Charged Particles (Interscience Publishers, Inc., New York, 1963), Part II. | en_US |
dc.identifier.citedreference | R. K. Osborn and E. H. Klevans, Ann. Phys. (N.Y.) 15, 105 (1961); E. Özizmir, Doctoral thesis, University of Michigan (1962); R. K. Osborn, Phys. Rev. 130, 2142 (1963). | en_US |
dc.identifier.citedreference | M. L. Goldberger and E. N. Adams, II, J. Chem. Phys. 20, 240 (1952). | en_US |
dc.identifier.citedreference | J. E. Mayer and W. Band, J. Chem. Phys. 15, 141 (1947). | en_US |
dc.identifier.citedreference | B. Kahn and G. E. Uhlenbeck, Physica 5, 399 (1938). | en_US |
dc.identifier.citedreference | H. S. Green, J. Chem. Phys. 19, 955 (1951). | en_US |
dc.identifier.citedreference | T. R. Hill, Statistical Mechanics (McGraw‐Hill Book Company, Inc., New York, 1956). | en_US |
dc.identifier.citedreference | G. E. Uhlenbeck and E. Beth, Physica 3, 729 (1936); 4, 915 (1937). For an excellent review of this subject, see J. de Boer, Rept. Progr. Phys. 12, 305 (1949). | en_US |
dc.owningcollname | Physics, Department of |
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