### Abstract

An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0) = f(x) e^{iS(x)/ℏ} in the semiclassical (ℏ → 0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.

Original language | English (US) |
---|---|

Pages (from-to) | 2185-2205 |

Number of pages | 21 |

Journal | Journal of Mathematical Physics |

Volume | 34 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1993 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Semiclassical mechanics for time-dependent Wigner functions.** / Robinson, Sam L.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 34, no. 6, pp. 2185-2205. https://doi.org/10.1063/1.530112

}

TY - JOUR

T1 - Semiclassical mechanics for time-dependent Wigner functions

AU - Robinson, Sam L

PY - 1993/1/1

Y1 - 1993/1/1

N2 - An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0) = f(x) eiS(x)/ℏ in the semiclassical (ℏ → 0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.

AB - An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0) = f(x) eiS(x)/ℏ in the semiclassical (ℏ → 0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.

UR - http://www.scopus.com/inward/record.url?scp=21144478964&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21144478964&partnerID=8YFLogxK

U2 - 10.1063/1.530112

DO - 10.1063/1.530112

M3 - Article

VL - 34

SP - 2185

EP - 2205

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

ER -