QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC) 5857 Wigner functions for curved spaces. I. On hyperboloids
QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC) 5857 Wigner functions for curved spaces. I. On hyperboloids
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量子力学（一般和非相对论）5857 弯曲空间的维格纳函数。
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
K. Wolf
中科院分区：
文献类型：
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作者：
M. Alonso;George S.Pogosyan;K. Wolf
我们提出了一个维格纳拟概率分布函数的哈密顿系统在常曲率空间，在这篇文章中的双曲面，它返回正确的边缘和协方差的夏皮罗函数下SO（D，1）变换。对于双曲面上服从Laplace-Beltrami方程的自由系统，我们在双曲坐标系中加入一个圆锥振子势。作为一个例子，我们分析了双曲线分支上的一维情况，其中圆锥振子是Poschl-Teller势。我们给出了解析解并绘制了计算结果。量子振子的标准理论在零曲率空间的收缩极限中得到恢复。
We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature, in this article on hyperboloids, which returns the correct marginals and has the covariance of the Shapiro functions under SO(D,1) transformations. To the free systems obeying the Laplace–Beltrami equation on the hyperboloid, we add a conic-oscillator potential in the hyperbolic coordinate. As an example, we analyze the one-dimensional case on a hyperbola branch, where this conic-oscillator is the Poschl–Teller potential. We present the analytical solutions and plot the computed results. The standard theory of quantum oscillators is regained in the contraction limit to the space of zero curvature.