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Construction of exact solutions to eigenvalue problems by the asymptotic iteration method

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Published 19 January 2005 • 2005 IOP Publishing Ltd
, , Citation Hakan Ciftci et al 2005 J. Phys. A: Math. Gen. 38 1147 DOI 10.1088/0305-4470/38/5/015

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1 Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal Québec, H3G 1M8, Canada

2 Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown PEI, C1A 4P3, Canada

3 Gazi Universitesi, Fen-Edebiyat Fakültesi Fizik Bölümü, 06500 Teknikokullar, Ankara, Turkey

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  1. Received 23 September 2004
  2. Published

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0305-4470/38/5/1147

Abstract

We apply the asymptotic iteration method (AIM) (Ciftci, Hall and Saad 2003 J. Phys. A: Math. Gen. 36 11807) to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue problems which includes Schrödinger problems with Coulomb, harmonic oscillator or Pöschl–Teller potentials, as well as the special eigenproblems studied recently by Bender et al (2001 J. Phys. A: Math. Gen. 34 9835) and generalized in the present paper to arbitrary dimension.

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