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

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, $g_{\mathrm{c}}^{(\ell )}$, of the coupling constant (strength), $g$, of the potential, $V(r)=-gv(r)$, for which a first $\ell$-wave bound state appears. These upper limits are significantly more stringent than hitherto known results.

7 pages

References in corpus (3)

• 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

Cited by in corpus (5)

• Exact solution of inverse-square-root potential $V\left(r\right)=-\frac{\alpha }{\sqrt{r}}$
• Transition states and the critical parameters of central potentials
• Long-range potential scattering: Converting long-range potential to short-range potential by tortoise coordinate
• Critical strength of attractive central potentials
• Upper and lower bounds on the mean square radius and criteria for occurrence of quantum halo states