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Orthogonal Functions

  • James B. Seaborn
Part of the Texts in Applied Mathematics book series (TAM, volume 8)

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)

Keywords

Hermite Polynomial Potential Energy Function Orthogonality Relation Fourier Amplitude Radial Wave Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    For real u n (z) complex conjugation is of no consequence.Google Scholar
  2. 2.
    In general, this is an infinite series, which we assume converges.Google Scholar
  3. 3.
    This development through Eq. (12.13) follows E. Merzbacher, op. cit. p. 81.Google Scholar
  4. 4.
    P.A.M. Dirac, Principles of Quantum Mechanics, Oxford University Press, Oxford, 1928, p. 58.Google Scholar
  5. 9.
    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.Google Scholar
  6. 17.
    This is the potential energy function in Yukawa’s meson theory of the nuclear force. It is called the Yukawa potential.Google Scholar
  7. 18.
    V.I. Kogan and V.M. Galitskiy, Problems in Quantum Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1963, p. 3.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • James B. Seaborn
    • 1
  1. 1.Department of PhysicsUniversity of RichmondUSA

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