Wigner Representation of Quantum Operators and Its Applications to Electrons in a Magnetic Field
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概要
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The Wigner representation F_s(p,q) of a quantum operator F(p,q) is defined by F_s(p,q)=hTrF(p,q)△(p-p,q-q) where △ is a quantum analogue of a delta function in the phase space. This gives in particular the Wigner distribution function for a density operator. Basic theorems are summarized for the computation rules for quantummechanical operators in the Wigner representation. This is applied, in particular, to electrons in a magnetic field, for which a Wigner d. f. is introduced to describe the distribution of physical momenta π^^→=mν^^→,ν^^← being the velocity, and the position x. This description has the advantage to avoid the use of a vector potential and so to be gauge-independent. As examples of application, the diamagnetism and the Hall effect are briefly treated. Further applications of this treatment will be published later.
- 社団法人日本物理学会の論文
- 1964-11-05
著者
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Kubo Ryogo
Department Of Physics Faculty Of Science And Technology Keio University
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Kubo Ryogo
Department Of Physics University Of Pennsylvania:(present) Department Of Physics University Of Tokyo
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