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Sufficient conditions for the existence of bound states in a central potential

Fabian Brau
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Abstract

We show how a large class of sufficient conditions for the existence of bound states, in non-positive central potentials, can be constructed. These sufficient conditions yield upper limits on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant (strength), $g$, of the potential, $V(r)=-g v(r)$, for which a first $\ell$-wave bound state appears. These upper limits are significantly more stringent than hitherto known results.

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Fabian Brau. 2004-11-02. Sufficient conditions for the existence of bound states in a central potential. https://doi.org/10.1088/0305-4470/37/26/006

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