Bateman's dual system revisited: quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator
type: Item
instance of: scholarly article
title: Bateman's dual system revisited: quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator
zbMATH Open document ID: 1064.81064
published in: Annals of Physics
publication date: 2004-08-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/quant-ph/0102128
review text: Recall that the connection between classical and quantum descriptions, established by Ehrenfest's theorems, is exact only for systems with quadratic Hamiltonians. The authors deal with a system of another sort, the 2D system of damped harmonic oscillator coupled to its time-reversed image (Bateman's dual system), the quantization of which used to plague with many conceptual problems. Here the quantization of the Bateman's dual system is made by applying the Feynman-Hibbs prescription for evolution amplitude. The time-dependent quantum states are constructed and discussed entirely in the framework of the classical theory. The corresponding geometric (Pancharatnam) phase is calculated and found to be directly related to the ground state energy of the 1D linear harmonic oscillator to which the 2D system reduces under appropriate constraint.
reviewed by: Yuri E. Gliklikh
Mathematics Subject Classification ID: 81Q70
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 2092922
zbMATH Keywords: quantization of dissipative systems
zbMATH Keywords: Feynman-Hibbs kernel formula
zbMATH Keywords: coherent states
zbMATH Keywords: geometric phases
zbMATH Keywords: 1D harmonic oscillator
author: Massimo Blasone
author: Petr Jizba
MaRDI profile type: Publication
OpenAlex ID: W1989523679
arXiv ID: quant-ph/0102128
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DOI: 10.1016/J.AOP.2004.01.008
description: scientific article