Four five-parametric and five four-parametric independent confluent Heun potentials for the stationary Klein-Gordon equation

Abstract

We present in total fifteen potentials for which the stationary Klein-Gordon equation is solvable in terms of the confluent Heun functions. Because of the symmetry of the confluent Heun equation with respect to the transposition of its regular singularities, only nine of the potentials are independent. Four of these independent potentials are five-parametric. One of them possesses a four-parametric ordinary hypergeometric sub-potential, another one possesses a four-parametric confluent hypergeometric sub-potential, and one potential possesses four-parametric sub-potentials of both hypergeometric types. The fourth five-parametric potential has a three-parametric confluent hypergeometric sub-potential, which is, however, only conditionally integrable. The remaining five independent Heun potentials are four-parametric and have solutions only in terms of irreducible confluent Heun functions.

References in corpus (4)

• On the Klein-Gordon oscillator subject to a Coulomb-type potential
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• The Lambert-W step-potential - an exactly solvable confluent hypergeometric potential
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Cited by in corpus (8)

• Solutions of the bi-confluent Heun equation in terms of the Hermite functions
• Schrödinger potentials solvable in terms of the general Heun functions
• A conditionally exactly solvable generalization of the inverse square root potential
• The third exactly solvable hypergeometric quantum-mechanical potential
• A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions
• Generalized confluent hypergeometric solutions of the Heun confluent equation
• Scalar resonant frequencies and Hawking effect of an $f(R)$ global monopole
• Exactly-solvable quantum systems in terms of Lambert-W functions