Wigner function and Schrodinger equation in phase-space representation (6 pages)

P. Campos, M.G.R. Martins, M.C.B. Fernandes +1 more

Dariusz Chruściński, Krzysztof Młodawski

We discuss a family of quasidistributions ($s$-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schr\"odinger equation. It turns out that although Wigner functions satisfy the Schr\"odinger equation in phase space, they have a completely different interpretation.

K. Kowalski, Jakub Rembieliński

Qian Shu Li, Gong Min Wei, Li Qiang Lü

This paper discusses the relationship between the Wigner function, along with other related quasiprobability distribution functions, and the probability density distribution function constructed from the wave function of the Schr\"odinger equation in quantum phase space, as formulated by Torres-Vega and Frederick (TF). At the same time, a general approach in solving the wave function of the Schr\"odinger equation of TF quantum phase space theory is proposed. The relationship of the wave functions between the TF quantum phase space representation and the coordinate or momentum representation is thus revealed.

Arturo Zúñiga-Segundo, H. M. Moya-Cessa, Francisco Soto

An explicit phase space representation of the wave function is build based on a wavelet transformation. The wavelet transformation allows us to understand the relationship between s − ordered Wigner function, (or Wigner function when s = 0), and the Torres-Vega-Frederick’s wave functions. This relationship is necessary to find a general solution of the Schrödinger equation in phase-space.

Wesley E. Brittin, Willard R. Chappell