Coherent distributions for the rigid rotator

M. Grigorescu

doi:10.1063/1.4953369

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arXiv · 1504.04832

Coherent distributions for the rigid rotator

M. Grigorescu

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Abstract

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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M. Grigorescu. 2015-04-19. Coherent distributions for the rigid rotator. https://doi.org/10.1063/1.4953369

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