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

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

2004-11-02

arxiv.org/abs/math-ph/0411008v1

J. Phys. A37, 6687 (2004)

Physics

Mathematical Physics

7 pages

Scientific paper

10.1088/0305-4470/37/26/006

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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