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

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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.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia

    S. I. Vinitsky, V. P. Gerdt, A. A. Gusev, V. A. Rostovtsev, V. N. Samoylov & T. V. Tupikova

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    M. S. Kaschiev

  3. Future University-Hakodate, Hakodate, 041-8655, Japan

    Y. Uwano

Authors
  1. S. I. Vinitsky
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  2. V. P. Gerdt
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  3. A. A. Gusev
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  4. M. S. Kaschiev
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  5. V. A. Rostovtsev
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  6. V. N. Samoylov
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  7. T. V. Tupikova
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  8. Y. Uwano
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Additional information

Original Russian Text © S.I. Vinitsky, V.P. Gerdt, A.A. Gusev, M.S. Kaschiev, V.A. Rostovtsev, V.N. Samoylov, T.V. Tupikova, Y. Uwano, 2006, published in Programmirovanie, 2006, Vol. 32, No. 2.

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Vinitsky, S.I., Gerdt, V.P., Gusev, A.A. et al. Symbolic algorithm for factorization of the evolution operator of the time-dependent Schrödinger equation. Program Comput Soft 32, 103–113 (2006). https://doi.org/10.1134/S0361768806020083

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  • DOI: https://doi.org/10.1134/S0361768806020083

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