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


  • 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.

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