Bound states of a quartic and sextic inverse-power-law potential for all angular momenta

Abstract

We use the tridiagonal representation approach to solve the radial Schrödinger equation for an inverse-power-law potential of a combined quartic and sextic degrees and for all angular momenta. The amplitude of the quartic singularity is larger than that of the sextic but the signs are negative and positive, respectively. It turns out that the system has a finite number of bound states, which is determined by the larger ratio of the two singularity amplitudes. The solution is written as a finite series of square integrable functions written in terms of the Bessel polynomial.