## Abstract

We study the asymptotic behavior of the ground-state wave function of multiparticle quantum systems without statistics in that region of configuration space where the particles break up into two well-defined clusters very far apart. One example of our results is the following: consider a system of N particles moving in three dimensions with rotationally invariant two-body potentials which are bounded and have compact support. Let D = C_{1},C_{2} be a partition into two clusters so that H(C_{1}) and H(C_{2}) have discrete ground states η_{1} and η_{2} of energy ϵ_{1} and ϵ_{2}. Suppose that Σ = ϵ_{1} + ϵ_{2} = inf σ_{ess}(H) and that H has a discrete ground state ϑ of energy E. Let ζ_{1}and ζ_{2} denote internal coordinates for the clusters C_{1} and c_{2} and let R be the difference of the centers of mass of the clusters. Let μ = M_{1}M_{2}/M_{1} + M_{2}with M_{i} the mass of clusters C_{i} and define k by k^{2}/2m = Σ-E. Then as R → a8 with ¦ζ_{i}¦ bounded, we prove that ϑ(ζ_{1},ζ_{2}, R) = cη(ζ_{1})η(ζ_{2})e^{−kR}R^{−1}(1+O(e^{−γR})) for some γ, c 〉 0. We prove weaker conclusions under weaker hypotheses, including results in the atomic case.

Original language | English (US) |
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Pages (from-to) | 324-343 |

Number of pages | 20 |

Journal | Advances in Applied Mathematics |

Volume | 1 |

Issue number | 3 |

DOIs | |

State | Published - 1980 |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics