Wigner functions

David K. Ferry, Xavier Oriols, Josef Weinbub

Tomer Bar-On

We construct a version of the discrete Wigner function (DWF) for any dimension. This DWF will be constructed from the continuous Wigner function (CWF). In addition, this DWF has many properties of the CWF.

David K. Ferry

The Wigner function has been studied for more than eight decades. Historically, it was developed from the Schrodinger wave equation, although it could have been developed on its own right. The use of the Wigner function is particularly important in scattering problems and clearly shows the transition to the classical world. In general, the Wigner function is not a positive definite function. One of the interesting aspects of the Wigner function is the ability to transfer many of the results of classical transport theory into quantum approaches merely by replacing the Boltzmann distribution with the Wigner function. The Wigner function for either of the two oscillators can be found by integrating out the coordinates of the other oscillator. Modern approaches with the Wigner function provide a distinct formulation that is recognized as equivalent to, but is a different alternative to normal operator-based quantum mechanics.

Sibel Başkal, Young S Kim, Marilyn E. Noz

Akiyoshi Takami, T. Hashimoto, M. Horibe +1 more

The Wigner functions on the one-dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum-mechanical expectation values in terms of Wigner functions are also discussed.

Jens Peder Dahl