## Abstract

A semiclassical initial value approximation for time-independent wave functions, previously derived for integrable systems, is rederived in a form which allows it to be applied to more general systems. The wave function is expressed as an integral over a Lagrangian manifold that is constructed by propagating trajectories from an initial manifold formed on a Poincaré surface. Even in the case of bound, integrable systems, it is unnecessary to identify action-angle variables or construct quantizing tori. The approximation is numerically tested for separable and highly chaotic two-dimensional quartic oscillator systems. For the separable (but highly anharmonic) system, the accuracy of the approximation is found to be excellent: overlaps of the semiclassical wave functions with the corresponding quantum wave functions exceed 0.999. For the chaotic system, semiclassical-quantum overlaps are found to range from 0.989 to 0.994, indicating accuracy that is still very good, despite the short classical trajectories used in the calculations.

Original language | English |
---|---|

Pages (from-to) | 51-61 |

Number of pages | 11 |

Journal | Chemical Physics |

Volume | 370 |

Issue number | 1-3 |

DOIs | |

State | Published - 12 May 2010 |

### Bibliographical note

Funding Information:This work was funded by the Israel Science Foundation .

### Funding

This work was funded by the Israel Science Foundation .

Funders | Funder number |
---|---|

Israel Science Foundation |

## Keywords

- Initial value representation
- Semiclassical approximations
- Semiclassical wave functions