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An improved shooting method for one-dimensional Schrödinger equation

✍ Scribed by Tomasz BŁeński; Jacques Ligou

Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
756 KB
Volume
50
Category
Article
ISSN
0010-4655

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✦ Synopsis

The phase function theory is used to improve the shooting method with the Noumerov finite difference scheme in application to finding bound states of the radial Schrodinger equation. The phase functions are constructed from Noumerov trial solutions which prevents the separate calculations of eigenvalues and eigenfunctions. The difference of the forward and backward phases is a monotomc function of the trial eigenvalue with zero at the eigenvalue. The radial quantum number is introduced as input in the phase difference. The discontinuity of the phase function with respect to the trial eigenvalue at singular points is used as diagnostics for the matching points. The modified shooting method with the Noumerov scheme and the phase function method connected with the first order nonlinear equation are compared in the numerical example.

leads to the same problems as the Noumerov References scheme in case of a wrong matching point.

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