Eur. Phys. J. Plus (2016) 131: 202
https://doi.org/10.1140/epjp/i2016-16202-8

Regular Article

Trigonometric potentials arising from the spheroidal equation: Supersymmetric partners and integral formulas

Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA

^* e-mail: axgeschu@iun.edu

Received: 6 March 2016
Accepted: 24 May 2016
Published online: 21 June 2016

Abstract

We construct supersymmetric partners of a quantum system featuring a class of trigonometric potentials that emerge from the spheroidal equation. Examples of both standard and confluent supersymmetric transformations are presented. Furthermore, we use integral formulas arising from the confluent supersymmetric formalism to derive new representations for single and multiple integrals of spheroidal functions.