Forced Time-Dependent Harmonic Oscillator in a Static Magnetic Field: Exact Quantum and Classical Solutions

Exact wave functions of the forced time-dependent two-dimensional harmonic oscillator in a static magnetic field are derived by unitary transformation. The geometrical phase induced by the driving force is the phase of the de Broglie wave associated with the particle moving according to the classical equation. Extending the idea of the Heisenberg correspondence principle to the time-dependent system, the exact classical solution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\dot \nu }$$ \end{document} obtained from quantum matrix elements.