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$ N$-body Schrödinger operators with finitely many bound states


Authors: W. D. Evans and Roger T. Lewis
Journal: Trans. Amer. Math. Soc. 322 (1990), 593-626
MSC: Primary 35P15; Secondary 35J10, 47F05, 81U10
MathSciNet review: 974515
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0974515-X
Article copyright: © Copyright 1990 American Mathematical Society