The non-relativistic Coulomb problem on a cone |
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Authors: | Gary W Gibbons Fernando Ruiz Ruiz Tanmay Vachaspati |
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Institution: | (1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, CB3 9EW Cambridge, UK;(2) Present address: Departamento de Física Teórica, Universidad Complutense, Madrid |
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Abstract: | 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. |
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