### Abstract

Quasi-energy spectral series ( epsilon _{nu}(h(cross)), Psi ( epsilon _{nu})) which, in the limit h(cross) to 0, correspond to stable motions of a classical system along closed phase trajectories are built up in terms of a quasi-classical approximation for the Schrodinger equation with an arbitrary T-periodic h(cross)^{-1} (pseudo)differential Hamilton operator. Using the procedure of splitting the quantum-mechanical phase into dynamic and geometric components, the "geometric" contribution of the Aharonov-Anandan phase gamma _{epsilon ( nu}) to the quasi-energy spectrum is calculated. It is shown that the gamma _{epsilon ( nu}) phase, in the adiabatic approximation, coincides with the Berry phase that corresponds to a cyclic evolution of a stable rest-point of a classical system. Some examples are considered.

Original language | English |
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Article number | 019 |

Pages (from-to) | 5653-5672 |

Number of pages | 20 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 28 |

Issue number | 19 |

DOIs | |

Publication status | Published - 1995 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

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## Cite this

*Journal of Physics A: Mathematical and General*,

*28*(19), 5653-5672. [019]. https://doi.org/10.1088/0305-4470/28/19/019