### Abstract

The ℏ→0 limit of the quantum dynamics determined by the Hamiltonian H(ℏ) = - (ℏ^{2}/2m)Δ + V on L ^{2}(ℝ^{n}) is studied for a large class of potentials. By convolving with certain Gaussian states, classically determined asymptotic behavior of the quantum evolution of states of compact support is obtained. For initial states of class C_{o} ^{1} the error terms are shown to have L^{2} norms of order ℏ^{1/2-∈} for arbitrarily small positive ∈.

Original language | English (US) |
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Pages (from-to) | 412-419 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 29 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics