量子态的非归一化准分布和层析图像
Unnormalized quasi-distributions and tomograms of quantum states
摘要：
断层图像和准分布函数，如维格纳，Glauber - Sudarshan $P$ -和Husimi $Q$ -函数，违反了标准的归一化条件。获得了使用这些断层图像和准分布函数重建密度矩阵的条件。研究了德布罗意平面波、Moschinsky快门问题和均匀恒定电场中带电粒子的定态等三种不同的状态。用Dirac δ函数、Airy函数和Fresnel积分表示的它们的层析图和准分布函数违反了标准的归一化条件，因而不能总是重建态的密度矩阵.
英文摘要：
Tomograms and quasi-distribution functions like Wigner, Glauber - Sudarshan $P$- and Husimi $Q$- functions that violate the standard normalization condition are considered. Conditions under which a reconstruction of the density matrix using these tomograms and quasi-distribution functions is possible are obtained. Three different examples of states like the de Broglie plane wave, the Moschinsky shutter problem and the stationary state of the charged particle in the uniform and constant electric field are studied. Their tomograms and quasi-distribution functions expressed in terms of the Dirac delta function, the Airy function and the Fresnel integrals are shown to violate the standard normalization condition and thus the density matrix of the state can not always be reconstructed.
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