Generating All Wigner Functions

@article{Curtright2001GeneratingAW,
  title={Generating All Wigner Functions},
  author={Thomas L. Curtright and Tsuneo Uematsu and C. Zachos},
  journal={Journal of Mathematical Physics},
  year={2001},
  volume={42},
  pages={2396-2415}
}
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasiprobability measure. The complete sets of Wigner functions necessary to expand all phase-space functions include off-diagonal Wigner functions, which may appear technically involved. Nevertheless, it is shown here that suitable generating functions of these complete sets can often be constructed, which are… Expand
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References

SHOWING 1-10 OF 61 REFERENCES
Features of time-independent Wigner functions
The Wigner phase-space distribution function provides the basis for Moyal{close_quote}s deformation quantization alternative to the more conventional Hilbert space and path integral quantizations.Expand
Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II. Quantitative analysis.
  • Han, Kim, Noz
  • Physics, Medicine
  • Physical review. A, General physics
  • 1989
TLDR
It is shown that the expectationvalue of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable, and parallel-axis theorems are established for the photon number and its variant. Expand
Phase space eigenfunctions of multidimensional quadratic hamiltonians
We obtain the explicit expressions for phase space eigenfunctions (PSE), i.e. Weyl's symbols of dyadic operators like |n > , |m > being the solution of the Schrodinger equation with the HamiltonianExpand
WIGNER TRAJECTORY CHARACTERISTICS IN PHASE SPACE AND FIELD THEORY
Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple - indeed, classical - for the quantized simple harmonicExpand
The Weyl representation in classical and quantum mechanics
Abstract The position representation of the evolution operator in quantum mechanics is analogous to the generating function formalism of classical mechanics. Similarly, the Weyl representation isExpand
The exact transition probabilities of quantum-mechanical oscillators calculated by the phase-space method
The ‘phase-space’ method in quantum theory is used to derive exact expressions for the transition probabilities of a perturbed oscillator. Comparison with the approximate results obtained byExpand
Quantum mechanics as a statistical theory
An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, theExpand
Quantization problem and variational principle in the phase‐space formulation of quantum mechanics
The problem of quantization in the phase‐space formulation of quantum mechanics is considered. An integral equation for the phase‐space eigenfunctions is derived which is equivalent to the standardExpand
Quantum mechanics without wave functions
The phase space formulation of quantum mechanics is based on the use of quasidistribution functions. This technique was pioneered by Wigner, whose distribution function is perhaps the most commonlyExpand
The formulation of quantum mechanics in terms of phase space functions
A relationship between the Hamiltonian of a system and its distribution function in phase space is sought which will guarantee that the average energy is the weighted mean of the Hamiltonian overExpand
...
1
2
3
4
5
...