Foundations of Electrodynamics

deGroot, S. R.; Suttorp, L. G.; Kazes, E.

doi:10.1119/1.1987928

Cited by 90 publications

(153 citation statements)

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“…The Wigner quasiprobability is the best compromise in quantum mechanics for a phase-space description of a quantum-mechanical state in analogy to the phase-space description in classical mechanics and statistics [30][31][32][33][34][35][36][37][38]. We consider one field mode corresponding to one mechanical degree of freedom and use a pair of canonical coordinates (q, p) or complex coordinates (α, α * ) and corresponding pairs of canonical operators (Q, P ) or boson annihilation and creation operator (a, a † ) in the following way…”

Section: Two-dimensional Radon and Fourier Transforms And Their Invermentioning

confidence: 99%

Radon transform and pattern functions in quantum tomography

Wünsche¹

1997

Journal of Modern Optics

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The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the last is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite polynomials which is appropriate for practical calculations. The structure of the pattern functions as first derivatives of the products of normalizable and nonnormalizable eigenfunctions to the number operator is considered from the point of view of this new representation.

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Section: Two-dimensional Radon and Fourier Transforms And Their Invermentioning

confidence: 99%

Radon transform and pattern functions in quantum tomography

Wünsche¹

1997

Journal of Modern Optics

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“…Phase space probability densities ρ(x, t) = ρ(X(x, −t), 0) evolve in classical mechanics in accord with the classical Liouville equation, Eq. (13). Consider that…”

Section: A Integrable Systems: Formal Correspondencementioning

confidence: 99%

“…where H = Equations (1) and (3) are of the following form in the Wigner-Weyl representation [13] [x = (p, q) denotes the collection of momenta p and coordinates q]…”

Section: Liouville Picture: the Correspondence Programmentioning

confidence: 99%

Quantum-classical correspondence via Liouville dynamics. I. Integrable systems and the chaotic spectral decomposition

Wilkie

Brumer

1997

Phys. Rev. A

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A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the cancellation of essential singularities, is demonstrated. The application to chaotic systems requires an understanding of classical Liouville eigenfunctions and a Liouville spectral decomposition, developed herein. General approaches to the construction of these Liouville eigenfunctions and classical spectral projectors in quantum and classical mechanics are discussed and are employed to construct Liouville eigenfunctions for classically chaotic systems. Correspondence for systems whose classical analogs are chaotic is discussed, based on this decomposition, in the following paper [1].

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“…The use of the reflection coeflacient allows the dielectric measurement of buried material and possibly the reconstruction of the geometry of buried objects such as archaeological artifacts, pipes, conduit, or land mines [77][78][79][80][81][82][83] 30 GHz. In these methods the TEM mode transmission and reflection coefficients are measured using algorithms similar to those used in closed transmission lines to obtain the material properties [84][85][86][87].…”

Section: Csc(m)mentioning

confidence: 99%