Gradient symplectic algorithms for solving the radial Schrodinger equation. Academic Article

abstract

• 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 gradient symplectic algorithms is particularly suited for solving harmonic-oscillator dynamics. By use of Suzuki's rule [Proc. Jpn. Acad., Ser. B: Phys. Biol. Sci. 69, 161 (1993)] 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 [J. Phys. A 18, 245 (1985)] of backward Newton-Ralphson iterations.

authors

• Chin, Siu

published proceedings

• J Chem Phys

author list (cited authors)

• Chin, S. A., & Anisimov, P.

citation count

• 15

complete list of authors

• Chin, Siu A||Anisimov, Petr

publication date

• February 2006

publisher

• AIP Publishing  Publisher

published in

• Journal of Chemical Physics  Journal

keywords

• 0101 Pure Mathematics

PubMed Central ID

• 16468850

Digital Object Identifier (DOI)

• 10.1063/1.2150831

start page

• 054106

end page

• 054106

volume

• 124

issue

• 5

URL

• http://dx.doi.org/10.1063/1.2150831