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Orthogonal Polynomials pp 217–228Cite as

The Recursion Method and the Schroedinger Equation

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Part of the book series: NATO ASI Series ((ASIC,volume 294))

Abstract

The use of generalized orthogonal polynomials is described for the calculation of quantum mechanical properties of physical systems. Quantum mechanics and its mathematical representation are reviewed. Expressions for various physical quantities are related to the orthogonal polynomials obtained from the action of an observable on particular states. Polynomial sets for which weight distributions are known may be used as exact models form which the solutions of other models may be approximated by perturbations. The finite precision, orthogonal polynomial can be constructed numerically even for infinite dimensional models.

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References

  1. . P. A. M. Dirac, “The Principles of Quantum Mechanics,” Oxford University Press, 1947.

    Google Scholar 

  2. F. Cyrot-Lackmann, J. Phys. (Paris), Suppl. C1, 67(1970).

    Google Scholar 

  3. . J. A. Shohat and J.D. Tamarkin, “The Problem of Moments,” Math. Surv. I, rev. ed., Am. Math. Soc., Providence Rhode Island, 1950.

    Google Scholar 

  4. R. Haydock, Solid State Physics 35, Academic Press, New York, 215(1980)

    Google Scholar 

  5. C. Lanczos, J. Res. Nat. Bur. Stand. 45, 255(1950).

    Google Scholar 

  6. . T. S. Chihara, “An introduction to Orthogonal Polynomials,” Gordon and Breach, New York, 1978.

    Google Scholar 

  7. R. Haydock, Phi. Mag. 53, 545(1986).

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  8. W. M. C. Foulkes and R. Haydock, J. Phys. C. 19, 6573(1986).

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  9. . B. N. Parlett, “The Symmetric Eigenvalue Problem,” Prentice Hall, Englewood Cliffs, N. J., 1980.

    Google Scholar 

  10. R. Haydock, Comp. Phys. Comm. 53, 133(1989).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics & Materials Science Institute, University of Oregon, Eugene, 97403, OR, USA

    Roger Haydock

Authors
  1. Roger Haydock
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, Ohio, USA

    Paul Nevai

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© 1990 Kluwer Academic Publishers

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Haydock, R. (1990). The Recursion Method and the Schroedinger Equation. In: Nevai, P. (eds) Orthogonal Polynomials. NATO ASI Series, vol 294. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0501-6_10

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  • DOI: https://doi.org/10.1007/978-94-009-0501-6_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6711-9

  • Online ISBN: 978-94-009-0501-6

  • eBook Packages: Springer Book Archive

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