On the Function in Quantum Mechanics Which Corresponds to a Given Function in Classical Mechanics

McCoy, Neal H.

doi:10.1073/pnas.18.11.674

Cited by 90 publications

(39 citation statements)

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“…By integrating it over ~, fi, 7, u and multiplying it with r 2 p~ we obtain the function Fls(l'(r, p )=16 r2 p~ exp (-2~r~) exp (34) which is normalized such that oo Go ~ Fls(a)(r,p) dr dp= 1. It is obvious that Fls(1)(r,p) gives us complete information about the ls state in the single gaussian approximation.…”

Section: The Single Gaussian Approximation To the Ls Statementioning

confidence: 99%

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Wigner's phase space function and atomic structure

Dahl

Springborg

1982

Molecular Physics

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We have constructed the Wigner function for the ground state of the hydrogen atom and analysed its variation over phase space. By means of the Weyl correspondence between operators and phase space functions we have then studied the description of angular momentum and resolved a dilemma in the comparison with early quantum mechanics. Finally we have discussed the introduction of local energy densities in coordinate space and demonstrated the validity of a local virial theorem.

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Section: The Single Gaussian Approximation To the Ls Statementioning

confidence: 99%

“…These expressions were first derived by McCoy [34]. Using the commutation relation Thus, there is a difference of ~-h 2 between the Weyl transform of l e and the ordinary quantum mechanical operator 12.…”

Section: The Weft Correspondencementioning

confidence: 99%

Wigner's phase space function and atomic structure

Dahl

Springborg

1982

Molecular Physics

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“…The reason for these controversies is the non-trivial relation between quantum states and the experimentally observable statistics of physical properties. It was already noticed in the early days of quantum mechanics that quantum states can be represented by quasi-probabilities that closely resemble phase space distributions of two conjugate variables which are represented by non-commuting operators in the Hilbert space formalism [6][7][8][9]. In these quasi-probabilities, the non-classical correlations between physical properties represented by non-commuting Hilbert space operators are represented by the non-positive joint probabilities assigned to the possible combinations of eigenvalues for the two observables.…”

Section: Introductionmentioning

confidence: 99%

Observation of non-classical correlations in sequential measurements of photon polarization

2016

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A sequential measurement of two non-commuting quantum observables results in a joint probability distribution for all output combinations that can be explained in terms of an initial joint quasiprobability of the non-commuting observables, modified by the resolution errors and back-action of the initial measurement. Here, we show that the error statistics of a sequential measurement of photon polarization performed at different measurement strengths can be described consistently by an imaginary correlation between the statistics of resolution and back-action. The experimental setup was designed to realize variable strength measurements with well-controlled imaginary correlation between the statistical errors caused by the initial measurement of diagonal polarizations, followed by a precise measurement of the horizontal/vertical polarization. We perform the experimental characterization of an elliptically polarized input state and show that the same complex joint probability distribution is obtained at any measurement strength.

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“…which is essentially the modern definition that will be given below (formula (9) ( X P + P X ) and one finds that more generally [25] …”

Section: Discussion Of Quantizationmentioning

confidence: 99%

Born–Jordan quantization and the uncertainty principle

Gosson

2013

J. Phys. A: Math. Theor.

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The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, the idea of which goes back to Born and Jordan, and which has recently been revived in another context, namely time-frequency analysis. We show in particular that the uncertainty principle does not enjoy full symplectic covariance properties in the Born and Jordan scheme, as opposed to what happens in the Weyl quantization.

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On the Function in Quantum Mechanics Which Corresponds to a Given Function in Classical Mechanics

Cited by 90 publications

References 0 publications

Wigner's phase space function and atomic structure

Wigner's phase space function and atomic structure

Observation of non-classical correlations in sequential measurements of photon polarization

Born–Jordan quantization and the uncertainty principle

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