Bound states of a quartic and sextic inverse-power-law potential for all angular momenta
Saudi Center for Theoretical Physics, P.O. Box 32741, 21438, Jeddah, Saudi Arabia
2 Department of Physics and Physical Oceanography, Memorial University of Newfoundland, A1B 3X7, St. John’s, NL, Canada
3 Mathematical Modeling and Numerical Simulation Laboratory, Badji Mokhtar University, BP 12, Annaba, Algeria
Accepted: 10 April 2021
Published online: 25 April 2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021