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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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$N$-body Schrödinger operators with finitely many bound states
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by W. D. Evans and Roger T. Lewis PDF
Trans. Amer. Math. Soc. 322 (1990), 593-626 Request permission

Abstract:

In this paper we consider a class of second-order elliptic operators which includes atomic-type $N$-body operators for $N > 2$. Our concern is the problem of predicting the existence of only a finite number of bound states corresponding to eigenvalues below the essential spectrum. We obtain a criterion which is natural for the problem and easy to apply as is demonstrated with various examples. While the criterion applies to general second-order elliptic operators, sharp results are obtained when the Hamiltonian of an atom with an infinitely heavy nucleus of charge $Z$ and $N$ electrons of charge $1$ and mass $\tfrac {1} {2}$ is considered.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 322 (1990), 593-626
  • MSC: Primary 35P15; Secondary 35J10, 47F05, 81U10
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0974515-X
  • MathSciNet review: 974515