On coherent-state representations of quantum mechanics: Wave mechanics in phase space

Møller, Klaus Braagaard; Jørgensen, Thomas Godsk; Torres-Vega, Gabino

doi:10.1063/1.473684

Cited by 44 publications

(34 citation statements)

References 29 publications

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“…The phase-space description of quantum mechanics is also useful for investigating quantum chemical systems (Tortes-Vega, 1993a, b;Tones-Vega andFrederick, 1990, 1993;Harriman, 1994;Wlodarz, 1994;Moiler et al, 1997). Furthermore, an uncertainty relation, called the operational uncertainty relation (W6dkiewicz, 1987), is established in the operational phase-space measurement.…”

Section: Introductionmentioning

confidence: 98%

State change, quantum probability, and information in operational phase-space measurement

Ban

1997

Int J Theor Phys

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State change, quantum probability, and information gain in the operational phasespace measurement are formulated by means of positive operator-valued measure (POVM) and operation. The properties of the operational POVM and its marginal POVM which yield the quantum probability distributions of the measurement outcomes obtained by the operational phase-space measurement are investigated. The Naimark extension of the operational POVM can be expressed in terms of the relative-position states and the relative-momentum states in the extended Hilbert space. An observable quantity measured in the operational phase-space measurement becomes a fuzzy or unsharp observable. The state change of a physical system caused by the operational phase-space measurement is described by the operation which is obtained explicitly for the position and momentum measurements and for the simultaneous measurement of position and momentum. Using the results, the entropy change of the measured physical system and the information gain in the operational phase-space measurement are investigated. It is found that the average value of the entropy change is equal to the Shannon mutual information extracted from the outcomes exhibited by the measurement apparatus.

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Section: Introductionmentioning

confidence: 98%

State change, quantum probability, and information in operational phase-space measurement

Ban

1997

Int J Theor Phys

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“…However, usage of the well-known technique of displacement operators is in spirit closer to the construction of the usual position and momentum representations and, also, it provides a more transparent physical interpretation of the auxiliary state as a ''probe'' state in phase space. 8 With this interpretation, phase-space representation of quantum state vectors becomes a powerful tool and has been applied recently in the study of quantum dynamics directly in phase space 9 or as a route to semiclassical approximations.…”

Section: Displacement-operator Approachmentioning

confidence: 99%

“…In general, a displacement operator that displaces the expectation values of the position and momentum for any state by r and k simultaneously, can be defined as 7,8 …”

Section: Displacement-operator Approachmentioning

confidence: 99%

“…The displacement-operator approach is essentially equivalent to the coherent-state formalism as put forward by, for instance, Klauder and Skagerstam 7 and studied in some detail by the present author. 8 Hence, the presentation given here is extracted from these earlier works and put in a form relevant for the present discussion. For a thorough review and analysis of the use of displacement operators, the reader is referred to Refs.…”

Section: Introductionmentioning

confidence: 99%

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Comment on phase-space representation of quantum state vectors

Møller

1999

Journal of Mathematical Physics

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A simple approach to phase-space representation of quantum state vectors using the displacement-operator formalism is presented. Although the resulting expressions for the fundamental operators ͑position and momentum͒ are equivalent to those obtained by other methods, this approach provides both alternative mathematical foundation as well as physical interpretation of phase-space representation of quantum state vectors.

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“…The formalism in equations (1) to (4) was suggested ( [5], [8]) by the properties of coherent states. In their generalized form these are [9] |p, q; σ ≡D [p, q] |σ ,…”

Section: Introductionmentioning

confidence: 99%

Wavefunctions on phase space

Smith¹

2006

J. Phys. A: Math. Gen.

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Theories of , Harriman [6], and of Ban [11], in which phase space points (p,q) are used as configurational variables to formulate quantum mechanics are considered from the standpoint of a class of quantization schemes associating phase space functions with operators. The connection between these schemes and the theories given in [5] to [11] is made by means of augmented wave functions ψ (λ) σ (p, q; t), where λ = 0 corresponds to the ordering of Wigner and Weyl. For that case we use these functions to define a family of positive operator-valued measures for the phase angle of an harmonic oscillator.

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On coherent-state representations of quantum mechanics: Wave mechanics in phase space

Cited by 44 publications

References 29 publications

State change, quantum probability, and information in operational phase-space measurement

State change, quantum probability, and information in operational phase-space measurement

Comment on phase-space representation of quantum state vectors

Wavefunctions on phase space

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