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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 C. M. Bender and Q. Wang [J. Phys. A, Math. Gen. 34, 9835–9847 (2001; Zbl 1006.34076)] and generalized in the present paper to arbitrary dimension.
MSC:
34L40Particular ordinary differential operators
34A05Methods of solution of ODE
34A30Linear ODE and systems, general
81Q15Perturbation theories for operators and differential equations
81U052-body potential scattering theory (quantum theory)
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis