Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential

doi:10.1088/1674-1056/19/10/100309

Abstract Põschl–Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Pöschl–Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrödinger equation with PTDRSC potential are presented. The normalized φ, θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.

Keywords: Pöschl–Teller double-ring-shaped Coulomb potential supersymmetry and shape invariance Schrödinger equation bound states

Received: 15 July 2009
Revised: 23 February 2010
Accepted manuscript online:

PACS:	02.10.De	(Algebraic structures and number theory)
	02.10.Ud	(Linear algebra)
	03.65.Fd	(Algebraic methods)
	03.65.Ge	(Solutions of wave equations: bound states)

Fund: Project supported by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province of China (Grant No. 05KJD140252) and the Natural Science Foundation of Jiangsu Province of China (Grant No. KB2008199).

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Lu Fa-Lin(陆法林) and Chen Chang-Yuan(陈昌远) Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential 2010 Chin. Phys. B 19 100309

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Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential

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