中国物理B ›› 1999, Vol. 8 ›› Issue (1): 1-7.doi: 10.1088/1004-423X/8/1/001

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BERRY PHASES IN THE QUANTUM STATE OF THE ISOTROPIC HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

刘登云   

  1. Department of Physics, Shanxi Teachers University, Linfen 041004, China
  • 收稿日期:1998-07-13 出版日期:1999-01-15 发布日期:1999-01-20
  • 基金资助:
    Project supported by the Shanxi Provincial Foundation for Returned Scholars.

BERRY PHASES IN THE QUANTUM STATE OF THE ISOTROPIC HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

Liu Deng-yun (刘登云)   

  1. Department of Physics, Shanxi Teachers University, Linfen 041004, China
  • Received:1998-07-13 Online:1999-01-15 Published:1999-01-20
  • Supported by:
    Project supported by the Shanxi Provincial Foundation for Returned Scholars.

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摘要： The problem of the isotopic harmonic oscillator of time-dependent frequency confined in a spherical box with time-dependent radius is studied. We show that the exact solution and the Lewis invariant operator can be obtained by performing two consecutive gauge transformations on the time-dependent Schr?dinger equation. On the basis of the exact solution the non-adiabatic Berry phases for the system are calculated.

Abstract: The problem of the isotopic harmonic oscillator of time-dependent frequency confined in a spherical box with time-dependent radius is studied. We show that the exact solution and the Lewis invariant operator can be obtained by performing two consecutive gauge transformations on the time-dependent Schr$\ddot{\rm o}$dinger equation. On the basis of the exact solution the non-adiabatic Berry phases for the system are calculated.

中图分类号:  (Foundations of quantum mechanics; measurement theory)

  • 03.65.Ta
03.65.Ge (Solutions of wave equations: bound states)