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Sturmian eigenvalue equations with a Chebyshev polynomial basis. (English) Zbl 0564.65059
From authors’ summary: A Chebyshev polynomial basis is proposed for the solution of Sturmian eigenvalue equations of the form \(Av=f\) which are encountered in quantum scattering theory. A is a non-self-adjoint second order differential operator and the solution is regular at the origin and has an outgoing wave condition asymptotically. Detailed computation of eigenvalues and eigenfunctions for five cases including analytical and physically realistic examples confirms the inherent polynomial stability of the method characteristic of the minimax norm.
Reviewer: T.Reginska

MSC:
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
81U05 \(2\)-body potential quantum scattering theory
34L99 Ordinary differential operators
Software:
EISPACK
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References:
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