## Abstract

The Herman-Kluk (HK) approximation for the propagator is derived semiclassically for a multidimensional system as an asymptotic solution of the Schrödinger equation. The propagator is obtained in the form of an expansion in h, in which the lowest-order term is the HK formula. Thus, the result extends the HK approximation to higher orders in h. Examination of the various terms shows that the expansion is a uniform asymptotic series and establishes the HK formula as a uniform semiclassical approximation. Successive terms in the series should allow one to improve the accuracy of the HK approximation for small h in a systematic and purely semiclassical manner, analogous to a higher-order WKB treatment of time-independent wave functions.

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

Pages (from-to) | 3-12 |

Number of pages | 10 |

Journal | Chemical Physics |

Volume | 322 |

Issue number | 1-2 |

DOIs | |

State | Published - 6 Mar 2006 |

### Bibliographical note

Funding Information:This work was supported by the Israel Science Foundation (Grant No. 85/03).

## Keywords

- Herman-Kluk theory
- Semiclassical approximations
- Time-dependent propagator