Communications in Mathematical Physics

, Volume 127, Issue 2, pp 295–312 | Cite as

The non-relativistic Coulomb problem on a cone

  • Gary W. Gibbons
  • Fernando Ruiz Ruiz
  • Tanmay Vachaspati


We study the non-relativistic Coulomb problem on a cone. The non-trivial topology of the cone breaks the symmetry associated with the conservation of the Lagrange-Laplace-Runge-Lenz vector. Classically this translates into a precession of the orbits, and quantum-mechanically into a splitting of the energy levels. For the scattering problem we find that classical multi-scattering is possible and that it gives rise to a wake structure; we also evaluate the full quantum wave function and from it recover the classical results.


Neural Network Statistical Physic Wave Function Energy Level Complex System 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Gary W. Gibbons
    • 1
  • Fernando Ruiz Ruiz
    • 1
  • Tanmay Vachaspati
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK

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