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Coulomb wave equation


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1: 33.2 Definitions and Basic Properties
§33.2(i) Coulomb Wave Equation
2: 33.14 Definitions and Basic Properties
§33.14(i) Coulomb Wave Equation
3: 33.22 Particle Scattering and Atomic and Molecular Spectra
§33.22(vi) Solutions Inside the Turning Point
4: 30.12 Generalized and Coulomb Spheroidal Functions
Generalized spheroidal wave functions and Coulomb spheroidal functions are solutions of the differential equation
5: 18.39 Applications in the Physical Sciences
(where the minus sign is often omitted, as it arises as an arbitrary phase when taking the square root of the real, positive, norm of the wave function), allowing equation (18.39.37) to be rewritten in terms of the associated Coulomb–Laguerre polynomials 𝐋 n + l 2 l + 1 ( ρ n ) . …
Discretized and Continuum Expansions of Scattering Eigenfunctions in terms of Pollaczek Polynomials: J-matrix Theory
6: 31.12 Confluent Forms of Heun’s Equation
This has regular singularities at z = 0 and 1 , and an irregular singularity of rank 1 at z = . Mathieu functions (Chapter 28), spheroidal wave functions (Chapter 30), and Coulomb spheroidal functions (§30.12) are special cases of solutions of the confluent Heun equation. …
7: Bibliography F
  • M. V. Fedoryuk (1989) The Lamé wave equation. Uspekhi Mat. Nauk 44 (1(265)), pp. 123–144, 248 (Russian).
  • C. Flammer (1957) Spheroidal Wave Functions. Stanford University Press, Stanford, CA.
  • V. A. Fock (1965) Electromagnetic Diffraction and Propagation Problems. International Series of Monographs on Electromagnetic Waves, Vol. 1, Pergamon Press, Oxford.
  • V. Fock (1945) Diffraction of radio waves around the earth’s surface. Acad. Sci. USSR. J. Phys. 9, pp. 255–266.
  • C. Fröberg (1955) Numerical treatment of Coulomb wave functions. Rev. Mod. Phys. 27 (4), pp. 399–411.
  • 8: Bibliography H
  • L. E. Hoisington and G. Breit (1938) Calculation of Coulomb wave functions for high energies. Phys. Rev. 54 (8), pp. 627–628.
  • M. H. Hull and G. Breit (1959) Coulomb Wave Functions. In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.), pp. 408–465.
  • J. Humblet (1984) Analytical structure and properties of Coulomb wave functions for real and complex energies. Ann. Physics 155 (2), pp. 461–493.
  • J. Humblet (1985) Bessel function expansions of Coulomb wave functions. J. Math. Phys. 26 (4), pp. 656–659.
  • C. Hunter and B. Guerrieri (1982) The eigenvalues of the angular spheroidal wave equation. Stud. Appl. Math. 66 (3), pp. 217–240.
  • 9: Software Index
    10: Bibliography N
  • R. G. Newton (2002) Scattering theory of waves and particles. Dover Publications, Inc., Mineola, NY.
  • T. D. Newton (1952) Coulomb Functions for Large Values of the Parameter η . Technical report Atomic Energy of Canada Limited, Chalk River, Ontario.
  • C. J. Noble and I. J. Thompson (1984) COULN, a program for evaluating negative energy Coulomb functions. Comput. Phys. Comm. 33 (4), pp. 413–419.
  • C. J. Noble (2004) Evaluation of negative energy Coulomb (Whittaker) functions. Comput. Phys. Comm. 159 (1), pp. 55–62.
  • J. F. Nye (1999) Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations. Institute of Physics Publishing, Bristol.