### Abstract

We describe several new techniques for obtaining detailed information on the exponential falloff of discrete eigenfunctions of N-body Schrödinger operators. An example of a new result is the bound (conjectured by Morgan) {Mathematical expression} for an eigenfunction ω of {Mathematical expression} with energy E_{N}. In this bound r_{1}r_{2}... r_{N} are the radii |x_{i}| in increasing order and the α's are restricted by α_{n}<(E_{n-1}-E_{n})^{1/2}, where E_{n}, for n=0, 1,..., N-1, is the lowest energy of the system described by H_{n}. Our methods include subharmonic comparison theorems and "geometric spectral analysis".

Original language | English (US) |
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Pages (from-to) | 1-34 |

Number of pages | 34 |

Journal | Communications In Mathematical Physics |

Volume | 64 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1978 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Deift, P., Hunziker, W., Simon, B., & Vock, E. (1978). Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems IV.

*Communications In Mathematical Physics*,*64*(1), 1-34. https://doi.org/10.1007/BF01940758