Bateman's dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator

Details Bateman's dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator Bateman's dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator

2001-02-26

arxiv.org/abs/quant-ph/0102128v2

Annals Phys. 312 (2004) 354-397

Physics

Quantum Physics

24 pages, RevTeX, 4 figures. Fully revised version

Scientific paper

10.1016/j.aop.2004.01.008

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.

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