On the corrector formulas for the numerical solution of the Schrödinger equation for central fields
Published online by Cambridge University Press: 24 October 2008
Extract
The evaluation of the eigenvalues and corresponding solutions of a Schrödinger equation is an ever-present problem in atomic and nuclear physics. For the numerical evaluation of the Schrödinger equation for a particle in a central potential, a useful corrector formula was derived by Douglas and Ridley ((5)) some years ago. Given a first estimate of the eigenvalue, this formula enables one to obtain a better estimate using any standard integration procedure for the differential equation. In a particular example, it was found ((5)) that it was necessary to start with an initial value which was accurate to about 10% in order that the procedure should converge to the desired eigenvalue, and that few iterations were required to obtain the eigenvalue with good precision.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 1 , January 1966 , pp. 79 - 82
- Copyright
- Copyright © Cambridge Philosophical Society 1966
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