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- Phase-space representation of quantum state vectors is a formulation of quantum mechanics elaborating the phase-space formulation with a Hilbert space. It "is obtained within the framework of the relative-state formulation. For this purpose, the Hilbert space of a quantum system is enlarged by introducing an auxiliary quantum system. Relative-position state and relative-momentum state are defined in the extended Hilbert space of the composite quantum system and expressions of basic operators such as canonical position and momentum operators, acting on these states, are obtained." Thus, it is possible to assign a meaning to the wave function in phase space, , as a quasiamplitude, associated to a quasiprobability distribution. The first wave-function approach of quantum mechanics in phase space was introduced by Torres-Vega and Frederick in 1990 (also see). It is based on a generalised Husimi distribution. In 2004 Oliveira et al. developed a new wave-function formalism in phase space where the wave-function is associated to the Wigner quasiprobability distribution by means of the Moyal product. An advantage might be that off-diagonal Wigner functions used in superpositions are treated in an intuitive way, , also gauge theories are treated in a operator form. (en)
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- 12873 (xsd:nonNegativeInteger)
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- Phase-space representation of quantum state vectors is a formulation of quantum mechanics elaborating the phase-space formulation with a Hilbert space. It "is obtained within the framework of the relative-state formulation. For this purpose, the Hilbert space of a quantum system is enlarged by introducing an auxiliary quantum system. Relative-position state and relative-momentum state are defined in the extended Hilbert space of the composite quantum system and expressions of basic operators such as canonical position and momentum operators, acting on these states, are obtained." Thus, it is possible to assign a meaning to the wave function in phase space, , as a quasiamplitude, associated to a quasiprobability distribution. (en)
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- Phase-space wavefunctions (en)
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