Critical strength of attractive central potentials

Abstract

We obtain several sequences of necessary and sufficient conditions for the existence of bound states applicable to attractive (purely negative) central potentials. These conditions yields several sequences of upper and lower limits on the critical value, $g_{\mathrm{c}}^{(\ell )}$, of the coupling constant (strength), $g$, of the potential, $V(r)=-gv(r)$, for which a first $\ell$-wave bound state appears, which converges to the exact critical value.

18 pages

References in corpus (6)

• Bound States in one and two Spatial Dimensions
• Upper and lower limits for the number of S-wave bound states in an attractive potential
• Necessary and sufficient conditions for existence of bound states in a central potential
• Upper and lower limits on the number of bound states in a central potential
• Generalization of the Calogero-Cohn Bound on the Number of Bound States
• Sufficient conditions for the existence of bound states in a central potential

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• Further developments for the auxiliary field method