Eur. Phys. J. D 17, 5-11 (2001)
https://doi.org/10.1007/s100530170032

Generation of exact analytic bound state solutions from solvable non-powerlaw potentials by a transformation method

¹ Physics Department, Gauhati University, Guwahati 781 014, India
² Physics Department, Assam Engineering College, Guwahati 781 013, India
³ Physics Department, Cotton College, Guwahati 781 001, India

Corresponding authors: ^a s_a_s_ahmed@hotmail.com sasa@guphys.cjb.net

Received: 30 August 2000
Revised: 16 March 2001
Published online: 15 October 2001

Abstract

A transformation method has been applied to the exactly solvable Hulthen problem to generate a hierarchy of exactly solved quantum systems in any chosen dimension. The generated quantum systems are, in general, energy-dependent with a single normalized eigenfunction, as the Hulthen potential is a non-powerlaw potential. A method has been devised to convert a subset of the generated quantum systems with energy-dependent potentials to a single normal system with an energy-independent potential that behaves like a potential qualitatively similar to the Poschl-Teller potential. A second-order application of the transformation method on the Hulthen system produces another Sturmian quantum system and a different method is given to regroup them into a normal quantum system which resembles the Morse potential. Existence of normalizable eigenfunctions for these systems are found to be dependent on the local and asymptotic behaviour of the transformation function.