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Discrete Variable Method for Non-Integrable Quantum Systems

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Quantum Systems in Chemistry and Physics Volume 2

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 2/3))

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Abstract

We present an effective numerical algorithm based on discrete variable techniques combined with finite elements for solving non-separable three-dimensional Schrödinger equations. By an additional discretization of the time propagator an effective algorithm is given for studying wave-packet propagation in simple systems. As examples we present applications to astrophysical and quantum chaological problems.

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References

  1. P. Faßbinder and W. Schweizer: Astron. Astrophys. 314, 700 (1996).

    Google Scholar 

  2. M.C. Gutzwiller: Chaos in Classical and Quantum Mechanics, Springer-Verlag, Berlin (1990).

    Google Scholar 

  3. H. Ruder, G. Wunner, H. Herold, and F. Geyer: Atoms in strong magnetic fields, Springer-Verlag, Berlin (1994).

    Google Scholar 

  4. J.C. Light, I.P Hamilton, and J.V. Lill; J. Chem. Phys. 82, 1400 (1985).

    Article  CAS  Google Scholar 

  5. G. Szegö: Orthogonal Polynomials, College Publication rev. ed. Am. Math. Soc., Providence, RI (1959).

    Google Scholar 

  6. R. Gonzaéz-Feréz and W. Schweizer: title, this volume.

    Google Scholar 

  7. W. Schweizer and P. Faßbinder: Comp. in Phys. 11, 641 (1997).

    Google Scholar 

  8. L.R. Ram-Mohan, S. Saigal, D. Dossa and J. Shertzer: Comp. in Phys. 1, 50 (1990).

    Google Scholar 

  9. Y. Saad: Numerical methods for large eigenvalues problems: theory and alghorithms, John Wiley & Sons. Inc., New York (1992).

    Google Scholar 

  10. T. Ericsson and A. Ruhe: Lanczos method for the numerical solution of large sparse generalized Math, of Comp. 35, 1251 (1980).

    Google Scholar 

  11. R.B. Lehoucq, D.C. Sorenson, and C. Yang: ARPACK users’ guide: Solution of large scale eigenvalue problems with implicitly restarted Arnoldi methods 1997.

    Google Scholar 

  12. D.C. Sorensen: SIAM J. Matr. Anal. Apps. 13, 357 (1992).

    Google Scholar 

  13. W. Schweizer, P. Faßbinder, R.M. González, M. Braun, S. Kulla and M. Stehle Journal of Computational and Applied Mathematics, special edition: Computational Astrophysics, 109, 95 (1999).

    Google Scholar 

  14. T. Regge: Nuovo Cim. 10, 544 (1958).

    Article  Google Scholar 

  15. V.S. Melezhik: Phys. Rev. A 48, 4528 (1993).

    Article  CAS  Google Scholar 

  16. K.A.U. Lindgren and J.T. Virtamo: J. Phys. B 12, 3465 (1979).

    Article  CAS  Google Scholar 

  17. P. Faßbinder and W. Schweizer: Phys. Rev. A 53, 2135 (1996).

    Google Scholar 

  18. J. Hanssen, R. McCarroll and P. Valiron: J. Phys. B 12, 89 (1979).

    Article  Google Scholar 

  19. E. Oks: Plasma Spectroscopy, Springer Series on Atoms and Plasma 9, Springer-Verlag, Berlin (1995).

    Google Scholar 

  20. I.P. Vinogradov, B. Jettkant, D. Meyer and K. Wiesemann: J. Phys. D 27, 1207 (1994).

    Article  CAS  Google Scholar 

  21. M.L. Naudeau, C. I. Sukenik, and P. H. Bucksbaum: Phys. Rev. A 56, 636 (1997).

    Article  CAS  Google Scholar 

  22. P. Faßbinder, W. Schweizer and T. Uzer: Phys. Rev. A 56, 3626 (1997).

    Google Scholar 

  23. M. Braun, W. Schweizer and H. Elster: Phys. Rev. A 57, 3739 (1998).

    Article  CAS  Google Scholar 

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© 2000 Kluwer Academic Publishers

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Schweizer, W., Faßbinder, P., González-Férez, R. (2000). Discrete Variable Method for Non-Integrable Quantum Systems. In: Hernández-Laguna, A., Maruani, J., McWeeny, R., Wilson, S. (eds) Quantum Systems in Chemistry and Physics Volume 2. Progress in Theoretical Chemistry and Physics, vol 2/3. Springer, Dordrecht. https://doi.org/10.1007/0-306-48145-6_16

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  • DOI: https://doi.org/10.1007/0-306-48145-6_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5970-8

  • Online ISBN: 978-0-306-48145-1

  • eBook Packages: Springer Book Archive

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