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Zbl 1069.34127
Ciftci, Hakan; Hall, Richard L.; Saad, Nasser
Construction of exact solutions to eigenvalue problems by the asymptotic iteration method. (English)
[J] J. Phys. A, Math. Gen. 38, No. 5, 1147-1155 (2005). ISSN 0305-4470

Summary: We apply the asymptotic iteration method (AIM) [Ciftci, Hall and Saad, J. Phys. A, Math. Gen. 36, No. 47, 11807--11816 (2003; Zbl 1070.34113)] 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 {\it C. M. Bender} and {\it Q. Wang} [J. Phys. A, Math. Gen. 34, 9835--9847 (2001; Zbl 1006.34076)] and generalized in the present paper to arbitrary dimension.

MSC 2000:: *34L40 Particular ordinary differential operators
34A05 Methods of solution of ODE
34A30 Linear ODE and systems
81Q15 Perturbation theories for operators and differential equations
81U05 2-body potential scattering theory
81Q10 Selfadjoint operator theory in quantum theory

Citations: Zbl 1070.34113; Zbl 1006.34076

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