Symbolic algorithm for factorization of the evolution operator of the time-dependent Schrödinger equation

Authors:
S. I. Vinitsky;V. P. Gerdt;A. A. Gusev;M. S. Kaschiev;V. A. Rostovtsev;V. N. Samoylov;T. V. Tupikova;Y. Uwano
Affiliations:
Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria;Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Joint Institute for Nuclear Research, Dubna, Moscow oblast, Russia 141980;Future University-Hakodate, Hakodate, Japan 041-8655
Venue:
Programming and Computing Software
Year:
2006

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Abstract

A symbolic algorithm for the decomposition of the unitary evolution operator is developed. This algorithm allows one to generate multilayer implicit schemes for solution of the time-dependent Schrödinger equation. Some additional gauge transformations are also implemented in the algorithm. This allows one to distinguish symmetric operators, which are required for constructing efficient evolutionary schemes. The efficiency of the generated schemes is demonstrated by integrable models.