Sufficient Conditions for an Attractive Potential to Possess Bound States. II

Abstract

A condition sufficient to secure the existence of a least one bound state for each angular momentum l ≤ L is given by the inequality $$-{\displaystyle \int }{}_0^{\infty }{\mathrm{d(qr)V(r)/[(qr)}}^{\text{2L}}{q}^2{\mathrm{-(qr)}}^{\text{−2L}}\text{V(r)]>1}$$ , where q is an arbitrary constant and V(r) an everywhere‐attractive potential.