Invariants for Time-Dependent Harmonic Oscillators from the Real Representation of Solution

• Authors: M. Liang , Z. Zhang , B. Yuan
• Languages of publication: EN

Abstracts

EN

The invariants for the time-dependent one-dimensional harmonic oscillator and the time-dependent two-dimensional harmonic oscillator in a static magnetic field are derived from the real representation of the exact solution to the equation of motion. Mathematically, the orthogonal functions invariant is the angular momentum of an isotropic time-dependent two-dimensional harmonic oscillator. Based on the invariants obtained here, the wave function for time-dependent two-dimensional harmonic oscillator in a static magnetic field in cylindrical coordinate is simply derived and the dynamical and geometrical phases are easily got by expressing the wave function as the superpositions of the wave functions of time-dependent two-dimensional harmonic oscillator in rectangular coordinate. For the driven system, the driving induced dynamical phase and the geometrical phase are respectively associated with the classical Hamiltonian and de Broglie wave of the center motion of the wave function.

Keywords

EN

45.20.Jj; 03.65.-w

Discipline

• 45.20.Jj: Lagrangian and Hamiltonian mechanics
• 03.65.-w: Quantum mechanics[see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics]

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2004
• Volume: 105
• Issue: 3
• Pages: 253-262

Dates

published

2004-03

received

2003-10-13

Contributors

author

M. Liang

• Department of Applied Physics, School of Science, Tianjin University, Tianjin 300072, China
• LiuHui Center for Applied Mathematics, Tianjin 300071, China

author

Z. Zhang

• Department of Applied Physics, School of Science, Tianjin University, Tianjin 300072, China

author

B. Yuan

• Department of Applied Physics, School of Science, Tianjin University, Tianjin 300072, China

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Identifiers

DOI

10.12693/APhysPolA.105.253