Wigner and Husimi Functions in Quantum Mechanics

Takahashi, Kin’ya

doi:10.1143/jpsj.55.762

Cited by 127 publications

(75 citation statements)

References 13 publications

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“…38.67.112.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://jcp.aip.org/jcp/copyright.jsp can be build into the equation of motion, and with the fiducial vector being a physically centred MUS ͑where the density is a Husimi function͒ the equation of motion for the density can be written as the classical Liouville equation plus correction terms. 10,32 For a potential of the kind…”

Section: Downloaded¬12¬jan¬2010¬to¬192mentioning

confidence: 99%

“…͑67͒, but only for a specific choice of such a fiducial vector the density as a whole will behave classically. 37 It is, furthermore, evident from the equation of motion of the Husimi function 10,32 that if the potential has non-vanishing derivatives of higher order than two no choice of MUS as fiducial vector will result in classical evolution of the phase-space density.…”

Section: Downloaded¬12¬jan¬2010¬to¬192mentioning

confidence: 99%

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

Møller

Jørgensen

Torres-Vega

1997

The Journal of Chemical Physics

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In this article we argue that the state-vector phase-space representation recently proposed by Torres-Vega and co-workers ͓introduced in J. Chem. Phys. 98, 3103 ͑1993͔͒ coincides with the totality of coherent-state representations for the Heisenberg-Weyl group. This fact leads to ambiguities when one wants to solve the stationary Schrödinger equation in phase space and we devise two schemes for the removal of these ambiguities. The physical interpretation of the phase-space wave functions is discussed and a procedure for computing expectation values as integrals over phase space is presented. Our formal points are illustrated by two examples. © 1997 American Institute of Physics. ͓S0021-9606͑97͒02317-9͔

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Section: Downloaded¬12¬jan¬2010¬to¬192mentioning

confidence: 99%

Section: Downloaded¬12¬jan¬2010¬to¬192mentioning

confidence: 99%

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

Møller

Jørgensen

Torres-Vega

1997

The Journal of Chemical Physics

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“…They have been defined canonically for several examples of classical phase spaces using the algebraic construction of Perelomov and Gilmore [7,8] and provide a representation of a quantum mechanical state by a positive normalized and bounded function on phase space -the so called Husimi function [9]. Let us mention in passing that the Husimi function was successfully applied to study dynamical properties of quantized chaotic systems [10,11].…”

Section: Introductionmentioning

confidence: 99%

Rényi-Wehrl entropies as measures of localization in phase space

Gnutzmann

Życzkowski

2001

J. Phys. A: Math. Gen.

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Abstract. We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these Rényi-Wehrl entropies for pure states for spin systems. According to Lieb's conjecture the minimal values are provided by the spin coherent states. Though Lieb's conjecture remains unproven, we give new proofs of partial results that may be generalized for other systems. We also investigate random pure states and calculate the mean Rényi-Wehrl entropies averaged over the natural measure in the space of pure quantum states.

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“…This autonomous path to quantization of the classical theory is based on the Wigner distribution function (WDF), ϱ W , which is defined by the Weyl transform of the density operator [4,9,10],…”

Section: Introductionmentioning

confidence: 99%

Phase-space description of the coherent state dynamics in a small one-dimensional system

et al. 2016

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Abstract:The Wigner-Moyal approach is applied to investigate the dynamics of the Gaussian wave packet moving in a double-well potential in the 'Mexican hat' form. Quantum trajectories in the phase space are computed for different kinetic energies of the initial wave packet in the Wigner form. The results are compared with the classical trajectories. Some additional information on the dynamics of the wave packet in the phase space is extracted from the analysis of the cross-correlation of the Wigner distribution function with itself at different points in time.

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Wigner and Husimi Functions in Quantum Mechanics

Cited by 127 publications

References 13 publications

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

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

Rényi-Wehrl entropies as measures of localization in phase space

Phase-space description of the coherent state dynamics in a small one-dimensional system

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