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Sturmian eigenvalue equations with a Bessel function basis. (English) Zbl 0585.34018
Summary: A non-self-adjoint Sturmian eigenvalue equation of the form \(Av=f\), encountered in quantum scattering theory, is solved as a complex general matrix eigenvalue problem. The matrix form is obtained on expansion of the solution in a discrete set of spherical Sturmian-Bessel functions of complex argument. This set of basis functions gives better convergence behavior for both the eigenvalues and eigenfunctions when compared to the results of a Chebyshev polynomial method reported previously.

34L99 Ordinary differential operators
81U10 \(n\)-body potential quantum scattering theory
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
Full Text: DOI
[1] DOI: 10.1103/RevModPhys.30.257 · doi:10.1103/RevModPhys.30.257
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