刚性转子的相干分布
Coherent distributions for the rigid rotator
AI总结：
本研究提出刚性转子经典刘维尔方程的相干解为正相空间分布，经形式离散化得到维格纳型准概率分布，其结果与各向异性转子量子化一致且含有限零点能，还揭示了准概率分布演化时量子波函数需满足含时薛定谔方程。
摘要：
刚性转子经典刘维尔方程的相干解被呈现为与哈密顿-雅可比理论的拉格朗日子流形相关的正相空间分布。通过对来自角动量傅里叶变换的左不变向量场进行形式离散化，这些解成为维格纳型准概率分布。结果与各向异性转子的通常量子化一致，但哈密顿量的期望值包含有限的“零点”能量项。研究表明，当准概率分布根据刘维尔方程演化时，相关量子波函数应满足含时薛定谔方程。
英文摘要：
Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions associated with the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite "zero point" energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schroedinger equation.
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