Perturbation theory in a framework of iteration methods

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Ciftci H. , Hall R., Saad N.

PHYSICS LETTERS A, vol.340, pp.388-396, 2005 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 340
  • Publication Date: 2005
  • Doi Number: 10.1016/j.physleta.2005.04.030
  • Title of Journal : PHYSICS LETTERS A
  • Page Numbers: pp.388-396
  • Keywords: asymptotic iteration method, perturbation series, eigenvalue problems, Schrodinger equation, SPHEROIDAL WAVE-FUNCTIONS, QUARTIC ANHARMONIC-OSCILLATOR, UNIFORM ASYMPTOTIC EXPANSIONS, SYMMETRIC QUANTUM-MECHANICS, STRONG-COUPLING EXPANSIONS, EIGENVALUE PROBLEMS, CUBIC OSCILLATOR, SCHRODINGER-EQUATION, HAMILTONIANS, ENERGY

Abstract

In a previous paper [J. Phys. A 36 (2003) 11807], we introduced the 'asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this Letter, we study perturbed problems in quantum mechanics and we use the method to find the coefficients in the perturbation series for the eigenvalues and eigenfunctions directly, without first solving the unperturbed problem. (c) 2005 Elsevier B.V. All rights reserved.