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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Asymptotic completeness for classes of two, three, and four particle Schrödinger operators
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by George A. Hagedorn PDF
Trans. Amer. Math. Soc. 258 (1980), 1-75 Request permission

Abstract:

Formulas for the resolvent ${(z - H)^{ - 1}}$ are derived, where $H = {H_0} + {\Sigma _{i < j}}{\lambda _{ij}}{V_{ij}}$ is an N particle Schrödinger operator with the center of mass motion removed. For a large class of two-body potentials and generic couplings $\{ {\lambda _{ij}}\}$, these formulas are used to prove asymptotic completeness in the $N \leqslant 4$ body problem when the space dimension is $m \geqslant 3$. The allowed potentials belong to a space of dilation analytic multiplication operators which fall off more rapidly than ${r^{ - 2 - \varepsilon }}$ at $\infty$. In particular, Yukawa potentials, generalized Yukawa potentials, and potentials of the form ${(1 + r)^{ - 2 - \varepsilon }}$ are allowed.
References
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 258 (1980), 1-75
  • MSC: Primary 81F10; Secondary 35P25
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0554318-4
  • MathSciNet review: 554318