Some nonclassical features of phase-space representations of quantum mechanics

Srinivas, M.; Wolf, Emil

doi:10.1103/physrevd.11.1477

Cited by 81 publications

(33 citation statements)

References 15 publications

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“…Early on, these were incorrectly conjectured to be the only such mixed states with positive Wigner function. The question of mixed states was given a full treatment in [24] and latter in [25]. Both references independently found that a theorem in classical probability attributed to Bochner [26] and generalization thereof can be used to characterize both the valid Wigner functions and the subset of positive ones.…”

Section: Review Of Wigner Functionsmentioning

confidence: 99%

Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation

Veitch¹,

Wiebe²,

Ferrie³

et al. 2013

New J. Phys.

100

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Section: Review Of Wigner Functionsmentioning

confidence: 99%

Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation

Veitch¹,

Wiebe²,

Ferrie³

et al. 2013

New J. Phys.

100

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“…Srinivas and Wolf [70] have proven Wigner's theorem still in a different way, yielding better insight into its physical significance. They, too, observe that operator R(q, p) in (1.165) must be a positive operator lest ρ(q, p) be positive for arbitrary density operators ρ.…”

Section: Proofmentioning

confidence: 99%

Foundations of Quantum Mechanics, an Empiricist Approach

Muynck¹

2002

146

291

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“…In order to unify the presentation, a phase space representation of both mechanics is used. Of the many equivalent quantal phase space representations (6), the Weyl correspondence (7) is used because, in this representation, the position and momentum operators are equal to their classical counterparts (8). In Sect.…”

Section: Introductionmentioning

confidence: 99%

A phase space moment method for classical and quantal dynamics

Turner¹,

Snider²

1981

Can. J. Phys.

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A hierarchy of translational moment equations for the position and momentum observables is considered. The resulting set of equations is truncated in a manner that includes only first and second order moments. This closure procedure is consistent with the conservation ofenergy and, for spherically symmetric potentials, with the conservation of angular momentum. The method is valid for both classical and quantal mechanics with the only difference being that for quantal systems, the dispersions in momentum and position must satisfy Heisenberg's uncertainty principle. With finite dispersion in the position, the average position and momentum do not satisfy Hamilton's equations of motion since the average acceleration is modulated by the variance-covariance in the position. For classical systems, the second order moments may be taken to zero in which case Hamilton's equations are obtained. For quantal systems, a comparision is made with Heller's Gaussian wave packet approach. The moment method is illustrated by applying it to the reflection of a phase space packet from a one dimensional repulsive inverse square potential. Applications to the calculation of collision cross sections are envisaged.On considere une gradation d'equations translationnelles des moments pour les observables position et impulsion. Le systeme d'equations obtenu est tronque d'une maniere qui inclut seulement les moments du premier et du second ordre. Ce procede de coupure est compatible avec la conservation de I'energie et, pour les potentiels a symetrie spherique, avec la conservation du moment cinetique. La methode est valide pour les deux mecaniques, classique et quantique, avec I'unique difference que les dispersions de I'impulsion et de la position doivent satisfaire, dans le cas de systemes quantiques, le principe d'incertitude de Heisenberg. Avec une dispersion finie dans la position, la position et I'impulsion moyennes ne satisfont pas les equations hamiltoniennes du mouvement, &ant donne que I'acceleration moyenne est modulee par la variance-covariance dans la position. Pour des systemes classiques, les moments du deuxieme ordre peuvent ktre pris egaux a zero, dans lequel cas on obtient les equations de Hamilton. Pour des systemes quantiques, on fait une comparaison avec la methode du paquet d'ondesgaussien de Heller. Pour illustrer la methode des moments, on I'applique au probleme de la reflexion d'un paquet d'onde dans I'espace de phase par un potentiel repulsif d'inverse carre en une dimension. On envisage des applications au calcul des sections efficaces de collision.

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Some nonclassical features of phase-space representations of quantum mechanics

Cited by 81 publications

References 15 publications

Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation

Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation

Foundations of Quantum Mechanics, an Empiricist Approach

A phase space moment method for classical and quantal dynamics

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