Non-commutative time-frequency tomography

Man’ko, V. I.; Mendes, R. Vilela

doi:10.1016/s0375-9601(99)00688-x

Cited by 130 publications

(97 citation statements)

References 14 publications

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“…If one has a pure state with the wave function Ψ (y), the marginal distribution has the form found in Ref. [36] w (X, µ, ν) = 1 2 π|ν|…”

Section: New Notion Of Quantum Statementioning

confidence: 89%

Conventional quantum mechanics without wave function and density matrix

Man’ko¹

1999

AIP Conference Proceedings

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The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schrödinger evolution equation and to the energy level equation written for the positive probability distribution are discussed. Instead of the transition probability amplitude (Feynman path integral) a transition probability is introduced. A new formulation of the conventional quantum mechanics (without wave function and density matrix) based on the "probability representation" of quantum states is given. An equation for the propagator in the new formulation of quantum mechanics is derived. Some paradoxes of quantum mechanics are reconsidered.

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“…If one has a pure state with the wave function Ψ (y), the marginal distribution has the form found in Ref. [36] w (X, µ, ν) = 1 2 π|ν|…”

Section: New Notion Of Quantum Statementioning

confidence: 89%

Conventional quantum mechanics without wave function and density matrix

Man’ko¹

1999

AIP Conference Proceedings

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“…A glance at the shape of the functions (13) shows that the nodes (the zero crossings) t n of the real (resp. imaginary) part of Ψ θ,T xn are the solutions of cos θ 2 sin θ t…”

Section: Tomograms and Signal Analysismentioning

confidence: 99%

A tomographic analysis of reflectometry data: I. Component factorization

Briolle

Lima

Man’ko

et al. 2009

Meas. Sci. Technol.

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Many signals in Nature, technology and experiment have a multicomponent structure. By spectral decomposition and projection on the eigenvectors of a family of unitary operators, a robust method is developed to decompose a signals in its components. Different signal traits may be emphasized by different choices of the unitary family. The method is illustrated in simulated data and on data obtained from plasma reflectometry experiments in the tore Supra.

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“…The dual symbol (18) provides the Husimi-Kano function Q(z). The reconstruction formula for the density state in terms of the Husimi-Kano function is just formula (19) with the replacement…”

Section: Diagonal Representation and Star-product Formalismmentioning

confidence: 99%

Superposition rule and entanglement in diagonal and probability representations of density states

Man’ko¹,

Marmo²,

Sudarshan³

2009

Phys. Scr.

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Abstract. The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the probability representation of quantum mechanics is reviewed. The connection of the diagonal and probability representations is discussed. The superposition rule is considered in terms of the density-operator symbols. The separability and entanglement properties of multipartite quantum systems are formulated as the properties of the density-operator symbols of the system states.

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Non-commutative time-frequency tomography

Cited by 130 publications

References 14 publications

Conventional quantum mechanics without wave function and density matrix

Conventional quantum mechanics without wave function and density matrix

A tomographic analysis of reflectometry data: I. Component factorization

Superposition rule and entanglement in diagonal and probability representations of density states

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