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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: 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. …
6: 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.
  • 7: 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.
  • 8: Software Index
    9: Bibliography T
  • T. Takemasa, T. Tamura, and H. H. Wolter (1979) Coulomb functions with complex angular momenta. Comput. Phys. Comm. 17 (4), pp. 351–355.
  • S. A. Teukolsky (1972) Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations. Phys. Rev. Lett. 29 (16), pp. 1114–1118.
  • I. J. Thompson and A. R. Barnett (1985) COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. Comput. Phys. Comm. 36 (4), pp. 363–372.
  • I. J. Thompson and A. R. Barnett (1986) Coulomb and Bessel functions of complex arguments and order. J. Comput. Phys. 64 (2), pp. 490–509.
  • I. J. Thompson (2004) Erratum to “COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments”. Comput. Phys. Comm. 159 (3), pp. 241–242.
  • 10: 13.28 Physical Applications
    §13.28(i) Exact Solutions of the Wave Equation
    The reduced wave equation 2 w = k 2 w in paraboloidal coordinates, x = 2 ξ η cos ϕ , y = 2 ξ η sin ϕ , z = ξ - η , can be solved via separation of variables w = f 1 ( ξ ) f 2 ( η ) e i p ϕ , where …and V κ , μ ( j ) ( z ) , j = 1 , 2 , denotes any pair of solutions of Whittaker’s equation (13.14.1). …
    §13.28(ii) Coulomb Functions