Abstract
In this paper we consider a class of second-order elliptic operators which includes atomic-type N N -body operators for N > 2 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 Z and N N electrons of charge 1 1 and mass 1 2 \tfrac {1} {2} is considered.
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