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Construction of exact solutions to eigenvalue problems by the asymptotic iteration method. (English) Zbl 1069.34127
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.

34L40Particular ordinary differential operators
34A05Methods of solution of ODE
34A30Linear ODE and systems, general
81Q15Perturbation theories for operators and differential equations
81U05$2$-body potential scattering theory (quantum theory)
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
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