Bound states of a quartic and sextic inverse-powerlaw 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.

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Cited by in corpus (4)

• Finite series representation for the bound states of a spiked isotropic oscillator with inverse-quartic singularity
• Electrostatic multipole contributions to the binding energy of electrons
• Progressive approximation of bound states by finite series of square-integrable functions
• An Accurate Zeroth-Order Perturbation Theory for Solving Power-Law Potentials within the Framework of the Asymptotic Iteration Method