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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.

MSC:
34L99 Ordinary differential operators
81U10 \(n\)-body potential quantum scattering theory
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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[1] DOI: 10.1103/RevModPhys.30.257 · doi:10.1103/RevModPhys.30.257
[2] DOI: 10.1007/BF01343196 · doi:10.1007/BF01343196
[3] DOI: 10.1098/rspa.1938.0093 · doi:10.1098/rspa.1938.0093
[4] DOI: 10.1016/0010-4655(82)90178-3 · doi:10.1016/0010-4655(82)90178-3
[5] DOI: 10.1103/PhysRevC.29.722 · doi:10.1103/PhysRevC.29.722
[6] DOI: 10.1103/PhysRevC.29.722 · doi:10.1103/PhysRevC.29.722
[7] DOI: 10.1016/0375-9474(84)90404-4 · doi:10.1016/0375-9474(84)90404-4
[8] DOI: 10.1103/PhysRevC.25.2196 · doi:10.1103/PhysRevC.25.2196
[9] DOI: 10.1103/PhysRevC.25.2196 · doi:10.1103/PhysRevC.25.2196
[10] DOI: 10.1103/PhysRevC.29.747 · doi:10.1103/PhysRevC.29.747
[11] DOI: 10.1103/PhysRevC.29.1153 · doi:10.1103/PhysRevC.29.1153
[12] DOI: 10.1016/0021-9991(85)90042-7 · Zbl 0564.65059 · doi:10.1016/0021-9991(85)90042-7
[13] DOI: 10.1007/BF02828869 · Zbl 0125.45604 · doi:10.1007/BF02828869
[14] DOI: 10.1007/BF02828869 · Zbl 0125.45604 · doi:10.1007/BF02828869
[15] DOI: 10.1007/BF02828869 · Zbl 0125.45604 · doi:10.1007/BF02828869
[16] DOI: 10.1103/PhysRevC.25.2196 · doi:10.1103/PhysRevC.25.2196
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