倘若我們選取 相干態(coherent state)為量子力學 希爾博特(Hilbert space) 向量空間的基地, 則我們發現其對應波函數(wave function)有與 韋恩-威爾變換(WignerWeyl’s transform) 相似的結構. 我們可以將 量力可量測(Obserable)在波函數的表示(representation)與 韋恩-威爾 上的表示視為僅為參數差1/2.另外,不論是量力的波函數表示,還是 韋恩-威爾 變換都有共容的古典極限.;We started with hbar = 1 in each different representation space said matrix representation on Hilbert space, realization as square integrable function and Wigner distribution. We introduced contraction parameter hbar by rescaled generator Q hat and P hat and consider their limitation i.e. hbar → 0 and showed comparable classical limit for each representation.
If coherent state has been chosen as base for our quantum Hilbert space, we found that correspond wave function (realization) have some star structure similar to Wigner-Weyl’s method and identify quantum observable algebra on both representation are equivalent up to a 1/2 factor.
