Some remarks on the nonnegative quantum-mechanical distribution function

Jannussis, A.; Patargias, N.; Leodaris, A.; Filippakis, P.; Filippakis, Th.; Streclas, A.; Papatheou, V.

doi:10.1007/bf02754621

Cited by 6 publications

(4 citation statements)

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“…Although this quantity is perhaps more familiar in the context of quantum field theory, [21][22][23] it will be seen to provide a useful description of a classical field as well (especially in the short-wavelength regime). The use of this representation for quantum mechanical wave functions has also become very popular [24][25][26][27][28] and is often referred to as a gaussian wavepacket representation. In fact, this representation will be shown to be closely related to the Weyl formalism and again this association is exploited in order to derive the phase-space equation governing it.…”

Section: -1-mentioning

confidence: 99%

“…We consider the coherent state or Glauber [21] representation which, although originally introduced for the study of the quantum theory of radiation and optics, has been recently applied [23][24][25][26][27][28] in other attempts to construct uniformly asymptotic quantum mechanical wave functions (where it is often called the gaussian wave-packet basis) and the study of chaotic quantum eigenfunctions. As has been our emphasis, however, we shall see that this representation has meaning and potential use in the analysis of short-wavelength solutions of classical wave equations as well.…”

Section: The Coherent State Representationmentioning

confidence: 99%

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Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves

1988

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Section: -1-mentioning

confidence: 99%

Section: The Coherent State Representationmentioning

confidence: 99%

Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves

1988

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“…The set of p , q , π p , π q now constitutes the Husimi representation [17]. The corresponding operationT on the Wigner equation will give the evolution equation of the Husimi positive functions as followŝ…”

Section: Becomes [15]mentioning

confidence: 99%

Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation

Bahrami¹

2008

SIGMA

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Abstract. In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mechanics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this representation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to Q-function.

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“…In 1932 the phase space picture of the quantum mechanics was introduced by the pioneering work of Wigner [15] and extended by Moyal [16], Hillary et al [17], Mehta [18], Agarwal and Wolf [19], Han et al [20] Kim and Wigner [21] and Jannussis et al [22], and many others. Although, the arguments invoked on the basis of the Heisenberg uncertainty principle made the physical meaning of the "phase space points" problematic, things have changed and phase space techniques mainly formulated by the theory of deformation quantization [23] and a family of Schrödinger equations in phase space [24,25,26,27,28] are now widely accepted and used.…”

Section: Introductionmentioning

confidence: 99%

Quantum Potential and Symmetries in Extended Phase Space

Nasiri¹

2006

SIGMA

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Abstract. The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space. It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation. The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one. The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation.

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Some remarks on the nonnegative quantum-mechanical distribution function

Cited by 6 publications

References 0 publications

Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves

Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves

Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation

Quantum Potential and Symmetries in Extended Phase Space

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