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Title: Coherent distributions for the rigid rotator

Abstract

Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on 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 Schrödinger equation.

Authors:
 [1]
  1. CP 15-645, Bucharest 014700 (Romania)
Publication Date:
OSTI Identifier:
22596852
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; BOLTZMANN-VLASOV EQUATION; FOURIER TRANSFORMATION; HAMILTONIANS; HAMILTON-JACOBI EQUATIONS; LAGRANGIAN FUNCTION; MATHEMATICAL SOLUTIONS; PHASE SPACE; QUANTIZATION; SCHROEDINGER EQUATION; TIME DEPENDENCE; VECTOR FIELDS; WAVE FUNCTIONS

Citation Formats

Grigorescu, Marius. Coherent distributions for the rigid rotator. United States: N. p., 2016. Web. doi:10.1063/1.4953369.
Grigorescu, Marius. Coherent distributions for the rigid rotator. United States. doi:10.1063/1.4953369.
Grigorescu, Marius. Wed . "Coherent distributions for the rigid rotator". United States. doi:10.1063/1.4953369.
@article{osti_22596852,
title = {Coherent distributions for the rigid rotator},
author = {Grigorescu, Marius},
abstractNote = {Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on 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 Schrödinger equation.},
doi = {10.1063/1.4953369},
journal = {Journal of Mathematical Physics},
number = 6,
volume = 57,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2016},
month = {Wed Jun 15 00:00:00 EDT 2016}
}