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Wigner Method in Quantum Statistical Mechanics

dc.contributor.authorİmre, Kayaen_US
dc.contributor.authorÖzizmir, Ercümenten_US
dc.contributor.authorRosenbaum, Marcosen_US
dc.contributor.authorZweifel, Paul Fredericken_US
dc.date.accessioned2010-05-06T23:14:24Z
dc.date.available2010-05-06T23:14:24Z
dc.date.issued1967-05en_US
dc.identifier.citationİmre, 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.urihttps://hdl.handle.net/2027.42/71122
dc.description.abstractThe 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.extent3102 bytes
dc.format.extent766628 bytes
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dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleWigner Method in Quantum Statistical Mechanicsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Nuclear Engineering, The University of Michigan, Ann Arbor, Michiganen_US
dc.contributor.affiliationumDepartment of Nuclear Engineering, The University of Michigan, Ann Arbor, Michiganen_US
dc.contributor.affiliationotherÇekmece Nuclear Research and Training Center, Istanbul, Turkeyen_US
dc.contributor.affiliationotherDepartment of Theoretical Physics, Middle East Technical University, Ankara, Turkeyen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/71122/2/JMAPAQ-8-5-1097-1.pdf
dc.identifier.doi10.1063/1.1705323en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceJ. von Neumann, Mathematical Foundation of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1955).en_US
dc.identifier.citedreferenceE. Wigner, Phys. Rev. 40, 749 (1932).en_US
dc.identifier.citedreferenceThere 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.citedreferenceIn 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.citedreferenceH. Weyl, The Theory of Groups and Quantum Mechanics (Dover Publications, New York, 1950).en_US
dc.identifier.citedreferenceH. J. Groenewold, Ref. 3; several properties of the Wigner method have been first given in this work.en_US
dc.identifier.citedreferenceThis approach has been used by I. Oppenheim and J. Ross, Phys. Rev. 107, 28 (1957).en_US
dc.identifier.citedreferenceL. Van Hove, Phys. Rev. 95, 249 (1954).en_US
dc.identifier.citedreferenceE. Fermi, Ric. Sci. 7, 13 (1938); G. C. Summerfield, Ann. Phys. (N.Y.) 26, 72 (1964).en_US
dc.identifier.citedreferenceB. 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.citedreferenceR. Nossal, Phys. Rev. 135, A1579 (1964).en_US
dc.identifier.citedreferenceR. Aamodt, K. M. Case, M. Rosenbaum, and P. F. Zweifel, Phys. Rev. 126, 1165 (1962).en_US
dc.identifier.citedreferenceHigher‐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.citedreferenceFor 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.citedreferenceR. 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.citedreferenceM. L. Goldberger and E. N. Adams, II, J. Chem. Phys. 20, 240 (1952).en_US
dc.identifier.citedreferenceJ. E. Mayer and W. Band, J. Chem. Phys. 15, 141 (1947).en_US
dc.identifier.citedreferenceB. Kahn and G. E. Uhlenbeck, Physica 5, 399 (1938).en_US
dc.identifier.citedreferenceH. S. Green, J. Chem. Phys. 19, 955 (1951).en_US
dc.identifier.citedreferenceT. R. Hill, Statistical Mechanics (McGraw‐Hill Book Company, Inc., New York, 1956).en_US
dc.identifier.citedreferenceG. 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.owningcollnamePhysics, Department of


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