On the Growth of the Number of Bound States with Increase in Potential Strength

Barry Simon

Type: Article

Publication Date: 1969-07-01

Citations: 25

DOI: https://doi.org/10.1063/1.1664948

Abstract

For a wide class of potentials, it is shown that N(λ), the number of bound states (including multiplicity) of −Δ + λV, obeys the conditions Aλ32 &lt; N(λ) &lt; Bλ32for λ sufficiently large. A and B are positive finite numbers. In the centrally symmetric cases, a related growth condition on lmax(λ), the largest l channel with bound states, is also obtained, namely, aλ12 &lt; lmax(λ) &lt; bλ12. Finally, we discuss analogous results for a larger class of central potentials and for the many-body case.

Locations

Journal of Mathematical Physics - View
CaltechAUTHORS (California Institute of Technology) - View - PDF

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+	Necessary condition for the existence of bound states	1965	P. Calogero
+	Growth properties of solutions of the reduced wave equation with a variable coefficient	1959	Tosio Kato
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+	On the Number of Bound States of a Given Interaction	1965	Gian Carlo Ghirardi A. Rimini
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+	Zur Spektraltheorie von Sturm-Liouville-Operatoren	1967	Joachim Weidmann
+	On the Scattering of a Particle by a Static Potential	1951	Res Jost A. Pais
+	On the Number of Bound States in a Central Field of Force	1966	J. H. E. Cohn
+	Sufficient Conditions for an Attractive Potential to Possess Bound States. II	1965	F. Calogero