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Coulomb potentials

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1: 17.17 Physical Applications
See Kassel (1995). … It involves q -generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials. …
2: 33.22 Particle Scattering and Atomic and Molecular Spectra
At positive energies E > 0 , ρ 0 , and: … R = m e c α 2 / ( 2 ) . …
κ = i Z 1 Z 2 α c ( m / ( 2 E ) ) 1 / 2 .
§33.22(vi) Solutions Inside the Turning Point
3: Bibliography H
  • R. L. Hall, N. Saad, and K. D. Sen (2010) Soft-core Coulomb potentials and Heun’s differential equation. J. Math. Phys. 51 (2), pp. Art. ID 022107, 19 pages.
  • 4: Bibliography C
  • B. C. Carlson and G. S. Rushbrooke (1950) On the expansion of a Coulomb potential in spherical harmonics. Proc. Cambridge Philos. Soc. 46, pp. 626–633.
  • 5: Bibliography S
  • M. J. Seaton (2002a) Coulomb functions for attractive and repulsive potentials and for positive and negative energies. Comput. Phys. Comm. 146 (2), pp. 225–249.
  • 6: 13.28 Physical Applications
    For potentials in quantum mechanics that are solvable in terms of confluent hypergeometric functions see Negro et al. (2000). …
    §13.28(ii) Coulomb Functions
    7: 5.20 Physical Applications
    Rutherford Scattering
    In nonrelativistic quantum mechanics, collisions between two charged particles are described with the aid of the Coulomb phase shift ph Γ ( + 1 + i η ) ; see (33.2.10) and Clark (1979). … Suppose the potential energy of a gas of n point charges with positions x 1 , x 2 , , x n and free to move on the infinite line - < x < , is given by
    5.20.1 W = 1 2 = 1 n x 2 - 1 < j n ln | x - x j | .
    5.20.2 P ( x 1 , , x n ) = C exp ( - W / ( k T ) ) ,
    8: Bibliography M
  • N. Michel and M. V. Stoitsov (2008) Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions. Comput. Phys. Comm. 178 (7), pp. 535–551.
  • N. Michel (2007) Precise Coulomb wave functions for a wide range of complex , η and z . Computer Physics Communications 176 (3), pp. 232–249.
  • C. Micu and E. Papp (2005) Applying q -Laguerre polynomials to the derivation of q -deformed energies of oscillator and Coulomb systems. Romanian Reports in Physics 57 (1), pp. 25–34.
  • 9: Bibliography B
  • A. R. Barnett (1981a) An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy. Comput. Phys. Comm. 21 (3), pp. 297–314.
  • K. L. Bell and N. S. Scott (1980) Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.
  • M. V. Berry (1966) Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.
  • A. Bhattacharjie and E. C. G. Sudarshan (1962) A class of solvable potentials. Nuovo Cimento (10) 25, pp. 864–879.
  • J. C. Bronski, L. D. Carr, B. Deconinck, J. N. Kutz, and K. Promislow (2001) Stability of repulsive Bose-Einstein condensates in a periodic potential. Phys. Rev. E (3) 63 (036612), pp. 1–11.