### Abstract

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture are developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in turn provide means to compute quantum corrections to the symplectic structure of an effective system.

Original language | English (US) |
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Pages (from-to) | 713-745 |

Number of pages | 33 |

Journal | Reviews in Mathematical Physics |

Volume | 18 |

Issue number | 7 |

DOIs | |

State | Published - Aug 2006 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Bojowald, M., & Skirzewski, A. (2006). Effective equations of motion for quantum systems.

*Reviews in Mathematical Physics*,*18*(7), 713-745. https://doi.org/10.1142/S0129055X06002772