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Zbl 0728.35075
Evans, W.D.; Lewis, R.; Saitó, Y.
Finiteness of bound states of general N-body operators. (English)
[A] Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 159-162 (1990).

[For the entire collection see Zbl 0704.00019.] \par The article surveys some work of the authors on the problem of determining conditions which ensure that a general N-body operator has only a finite number of bound states. The results discussed apply to molecules as well as atoms. The underlying methods are the geometric technique of {\it S. Agmon} [``Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of N-body Schrödinger operators'', Mathematical Notes 29 (1982; Zbl 0503.35001)] for investigating Schrödinger operators with anisotropic potentials and that by the two first authors [``N-body Schrödinger operators with finitely many body states'', Trans. Am. Math. Soc. 322, No.2, 593-626 (1990; Zbl 0732.35062)] for breaking up the sesquilinear form which defines the operator. Further details and other developments are to appear elsewhere.
[W.D.Evans]

MSC 2000:: *35P05 General spectral theory of PDE
81U10 n-body potential scattering theory
35J10 Schroedinger operator

Keywords: finite number of bound states

Citations: Zbl 0704.00019; Zbl 0503.35001; Zbl 0732.35062

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