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- W1567470944 abstract "This is the Hamiltonian of an atom with an infinitely heavy nucleus of charge Z and N electrons of charge 1 and mass 1/2. Here x ∈ R is the coordinate of the ith electron and ∆i denotes the Laplacian in R with respect to the variable x. For the operator PN the next theorem gives a classic result. (For the appropriate references we refer the reader to the extensive reference list in [4] .) Theorem 1. (Zhislin (1960, 1969,1971), Uchiyama (1969) and others) The operator PN given by (1) has at most a finite number of bound states if and only if Z ≤ N − 1. In this paper we work towards a theory for general N-body operators which would include the results in Theorem 1 for atoms as well as results for molecules. A portion of this task has been accomplished in [2] for general atomic-type operators of the form" @default.
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- W1567470944 date "1990-01-01" @default.
- W1567470944 modified "2023-10-18" @default.
- W1567470944 title "Finiteness of bound states of general $n$-body operators" @default.
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