## Abstract

We determine the behavior in time of singularities of solutions to some Schrödinger equations on R^{n}. We assume the Hamiltonians are of the form H_{0}+V, where {Mathematical expression}, and where V is bounded and smooth with decaying derivatives. When all ω_{k}=0, the kernel k(t, x, y) of exp (-itH) is smooth in x for every fixed (t, y). When all ω_{1} are equal but non-zero, the initial singularity "reconstructs" at times {Mathematical expression} and positions x=(-1)^{m}y, just as if V=0;k is otherwise regular. In the general case, the singular support is shown to be contained in the union of the hyperplanes {Mathematical expression}, when ω_{j}t/π=l_{j} for j=j_{1},..., j_{r}.

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

Pages (from-to) | 1-26 |

Number of pages | 26 |

Journal | Communications in Mathematical Physics |

Volume | 90 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1983 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics