Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation

Details Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation

2005-09-27

arxiv.org/abs/physics/0509229v1

Physics

Computational Physics

19 pages, 10 figures

Scientific paper

10.1063/1.2150831

The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of {\it gradient} symplectic algorithms is particularly suited for solving harmonic oscillator dynamics. By use of Suzuki's rule for decomposing time-ordered operators, these algorithms can be easily applied to the Schrodinger equation. We demonstrate the power of this class of gradient algorithms by solving the spectrum of highly singular radial potentials using Killingbeck's method of backward Newton-Ralphson iterations.

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