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1: 33.22 Particle Scattering and Atomic and Molecular Spectra
At positive energies E > 0 , ρ 0 , and:
Attractive potentials: Z 1 Z 2 < 0 , η < 0 .
Repulsive potentials: Z 1 Z 2 > 0 , η > 0 .
R = m e c α 2 / ( 2 ) .
Attractive potentials: Z 1 Z 2 < 0 , r > 0 .
Repulsive potentials: Z 1 Z 2 > 0 , r < 0 .
Attractive potentials: Z 1 Z 2 < 0 , κ < 0 .
Repulsive potentials: Z 1 Z 2 > 0 , κ > 0 .
2: 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.
  • 3: Bibliography B
  • 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.
  • 4: Bibliography Y
  • K. Yang and M. de Llano (1989) Simple Variational Proof That Any Two-Dimensional Potential Well Supports at Least One Bound State. American Journal of Physics 57 (1), pp. 85–86.
  • F. L. Yost, J. A. Wheeler, and G. Breit (1936) Coulomb wave functions in repulsive fields. Phys. Rev. 49 (2), pp. 174–189.
  • 5: 18.39 Applications in the Physical Sciences
    defines the potential for a symmetric restoring force k x for displacements from x = 0 . … c) A Rational SUSY Potential argument The Schrödinger equation with potentialAs in this subsection both positive (repulsive) and negative (attractive) Coulomb interactions are discussed, the prefactor of Z / r in (18.39.43) has been set to + 1 , rather than the 1 of (18.39.28) implying that Z < 0 is an attractive interaction, Z > 0 being repulsive. … The weight functions for both the attractive and repulsive cases are now unit normalized, see Bank and Ismail (1985), and Ismail (2009). …