%0 Journal Article
%T Bateman's dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator
%A Massimo Blasone
%A Petr Jizba
%J Physics
%D 2001
%I arXiv
%R 10.1016/j.aop.2004.01.008
%X By using the Feynman-Hibbs prescription for the evolution amplitude, we quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. The time-dependent quantum states of such a system 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.
%U http://arxiv.org/abs/quant-ph/0102128v2