Analytic representations in quantum mechanics
Analytic representations in quantum mechanics
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量子力学中的解析表示
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
A. Vourdas
中科院分区：
文献类型：
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作者：
A. Vourdas
介绍了各种欧几里得、双曲和椭圆解析表示，并讨论了它们之间的关系。考虑了复平面上的巴格曼解析表示，并讨论了它与谐振子的其他相空间方法的关系。将解析函数的增长与其零点密度有关的一般理论应用于巴格曼函数，并由此得出了关于格劳伯相干态序列完备性的定理。介绍了基于SU（1,1）相干态和相态的单位圆盘上的两种双曲解析表示。本文还考虑了基于Barut-Girardello状态的复平面上的第三种解析表示，并研究了将其与其他解析表示相联系的变换。对于有限维Hilbert空间系统，介绍了扩展复平面上的椭圆解析表示和基于函数的解析表示。讨论了欧几里得、双曲和椭圆情况下的Berezin形式主义。并给出了这三种情况下的轮廓分析表示。
Various Euclidean, hyperbolic and elliptic analytic representations are introduced and relations among them are discussed. The Bargmann analytic representation in the complex plane is considered and its relation to other phase-space methods for the harmonic oscillator is reviewed. The general theory that relates the growth of analytic functions with the density of their zeros is applied to Bargmann functions and it leads to theorems on the completeness of sequences of Glauber coherent states. Two hyperbolic analytic representations in the unit disc, based on SU(1, 1) coherent states and also on phase states are introduced. A third analytic representation in the complex plane based on Barut–Girardello states is also considered and transformations which relate it to the other ones are studied. In the case of systems with finite-dimensional Hilbert space, an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced. The Berezin formalism in the Euclidean, hyperbolic and elliptic cases is discussed. Contour analytic representations in these three cases are also presented.