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1.2.1 Impulse response and coherent point-spread function 1.2.2 Mutual coherence function and cross-spectral density 1.2.3 Some basic examples of optical signals 1.3 Wigner distribution and ambiguity function 1.3.1 Definitions 1.3.2 Some basic examples again 1.3.3 Gaussian light 1.3.4 Local frequency spectrum 1.4 Some properties of the Wigner ...
Integration of the Wigner function over the momentum coordinate yields the spatial distribution function as is shown below. ρ(x):= ∫50 −51 W(x,p,n)dp x:= 0, 01 … 1 ρ ( x) := ∫ − 51 50 W ( x, p, n) d p x := 0, 01 … 1. The Wigner distribution can be used to calculate the expectation values for position, momentum and kinetic energy.
Hence, the phase-space distribution function introduced by Wigner [ 22] is the starting point for this phase-space picture of quantum mechanics. Widely known as the Wigner function, it is constructed from the Schrödinger wave function through the density matrix, a function of both position and momentum variables.
The Wigner Distribution. In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function W(q, p), the marginals of which yield the correct quantum probabilities for q and p ...
Figure 4: Wigner distribution of the above signal, represented as a surface and as contour curves. Please note the artifacts due to interferences. that is, the correct average is return only if the function whose average is desired can be split in two components, the first of which is function of tonly and the second of ωonly. If this ...
1 de ene. de 1997 · The Wigner distribution function (WDF) in quantum mechanics is a mathematical tool that correctly yields the expectation values of any function of the coordinates or the momenta. The chapter discusses WDF applications to the characterization of light fields and optical systems and to the problem of coupling optimization between sources and ...
简介. 维格纳分布(又名韦格纳分布，英文:Wigner Distribution Function,缩写为WDF) 是由1963年的 诺贝尔物理学奖 得主 尤金·维格纳 ，于1932年首次引用的一个新的方程式。. 众所皆知， 傅立叶变换 对于研究稳态 (时间独立)的讯号 (波形)是一项非常有用的工具，然而 ...
