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Orthogonal Functions

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Book cover Hypergeometric Functions and Their Applications

Part of the book series: Texts in Applied Mathematics ((TAM,volume 8))

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Abstract

In quantum mechanics, as well as other branches of physics, it is convenient to deal with complete sets of orthonormal functions. By orthonormal we mean that the functions have the property1

$$ \int {u_n^ * } (z){u_m}(z)dz = {\delta _{mn}}. $$
(12.1)

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References

  1. For real u n (z) complex conjugation is of no consequence.

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  2. In general, this is an infinite series, which we assume converges.

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  3. This development through Eq. (12.13) follows E. Merzbacher, op. cit. p. 81.

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  4. P.A.M. Dirac, Principles of Quantum Mechanics, Oxford University Press, Oxford, 1928, p. 58.

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  5. This velocity depends on the density of the membrane and on how tightly it is stretched. See A.L. Fetter and J.D. Walecka, op. cit. p. 273.

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  6. This is the potential energy function in Yukawa’s meson theory of the nuclear force. It is called the Yukawa potential.

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  7. V.I. Kogan and V.M. Galitskiy, Problems in Quantum Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1963, p. 3.

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Authors and Affiliations

  1. Department of Physics, University of Richmond, 23173, VA, USA

    James B. Seaborn

Authors
  1. James B. Seaborn
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© 1991 Springer Science+Business Media New York

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Seaborn, J.B. (1991). Orthogonal Functions. In: Hypergeometric Functions and Their Applications. Texts in Applied Mathematics, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5443-8_12

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  • DOI: https://doi.org/10.1007/978-1-4757-5443-8_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-3097-2

  • Online ISBN: 978-1-4757-5443-8

  • eBook Packages: Springer Book Archive

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