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The non-relativistic Coulomb problem on a cone

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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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References

  1. 't Hooft, G.: Commun. Math. Phys.117, 685 (1988)

    Article  Google Scholar 

  2. Deser, S., Jackiw, R.: Commun. Math. Phys.118, 495 (1988)

    Article  Google Scholar 

  3. Dowker, J.S.: J. Math. Phys.30, 770 (1989); Phys. Rev.D36, 3095 (1987)

    Article  Google Scholar 

  4. Linet, B.: Phys. Rev.D33, 1833 (1986)

    Article  Google Scholar 

  5. Brandenberger, R., Davis, A.C., Matheson, A.M.: Nucl. Phys.B307, 909 (1988)

    Article  Google Scholar 

  6. Smith, A.G.: Gravitational effects of an infinite straight cosmic string on classical and quantum fields: self-forces and vacuum fluctuations. TUFTS preprint TUTP-86-11 (1986)

  7. Ruback, P.J.: Nucl. Phys.B296, 669 (1988)

    Article  Google Scholar 

  8. Ruback, P.J., Shellard, E.P.: Phys. Lett.209B, 262 (1988)

    Google Scholar 

  9. Carlip, S.: Nucl. Phys.B324, 106 (1989)

    Article  Google Scholar 

  10. Lagrange, J.L.: Nouveau memoire de l'Academie Royale des Sciences et Belles Lettres de Berlin (1781), in Oeuvres de Lagrange, vol. 5, p. 132

  11. Deser, S., Jackiw, R., 't Hooft, G.: Ann. Phys.152, 220 (1984)

    Article  Google Scholar 

  12. Henneaux, M.: Phys. Rev.D29, 2766 (1984)

    Article  Google Scholar 

  13. Hankins, T.L.: Sir William Rowan Hamilton. Baltimore, MD: Johns Hopkins University Press 1983

    Google Scholar 

  14. Kay, B.S., Studer, U.M.: Quantum mechanics and field theory on cones and cosmic strings. University of Zurich and ETH preprint (1989)

  15. Silk, J., Vilenkin, A.: Phys. Rev. Lett.53, 1700 (1984)

    Article  Google Scholar 

  16. de Sousa Gerbert, Ph. Jackiw, R.: Commun. Math. Phys.124, 229–260 (1989)

    Article  Google Scholar 

  17. Sommerfeld, A.: Proc. Lond. Math. Soc.28, 417 (1897)

    Google Scholar 

Download references

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Author notes

  1. Fernando Ruiz Ruiz (MEC (Spain) Fellow)

    Present address: Departamento de Física Teórica, Universidad Complutense, Madrid

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, CB3 9EW, Cambridge, UK

    Gary W. Gibbons, Fernando Ruiz Ruiz (MEC (Spain) Fellow) & Tanmay Vachaspati

Authors
  1. Gary W. Gibbons
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  2. Fernando Ruiz Ruiz
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  3. Tanmay Vachaspati
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Communicated by L. Alvarez-Gaumé

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Gibbons, G.W., Ruiz, F.R. & Vachaspati, T. The non-relativistic Coulomb problem on a cone. Commun.Math. Phys. 127, 295–312 (1990). https://doi.org/10.1007/BF02096759

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  • DOI: https://doi.org/10.1007/BF02096759

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