Phase-integral treatment of the linear plus Coulomb potential. II: Expectation values and the probability density at the origin

Abstract The linear plus Coulomb potential V(r) = ar − b/r is considered. The first-, third-, and fifth-order phase-integral formulas for expectation values of integer powers of r are expressed in terms of complete elliptic integrals. It is pointed out how these results can be used to calculate the probability density close to the origin.