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Bound States in the Compactified Gravity


Affiliations
1 Institute for Condensed Matter Physics, The National Academy of Sciences of Ukraine, Lviv, Ukraine
 

A potential of pointlike mass in the partially compactified multidimensional space is considered. The problem is reduced to the multidimensional Poisson equation with the Dirac comb source in r.h.s. Explicit solutions are built in the cases of 2D and 4D spaces with one compact dimension. The last example of the potential is used in the Schrodinger equation. Bound states of a gravitating test particle on 3D brane of 4D compactified space are studied by means of various approximate methods.

Keywords

Gravitation, Compactification, Schrodinger Equation, Bound States.
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  • A. Erdelyi, Higher transcendental functions I (NY-Toronto-London, McGraw-Hill, 1953).
  • A.V. Marshakov, Physics-Uspekhi 45, 915 (2002).
  • D. Ivanenko and A. Sokolov, Klassische feldtheorie (Berlin, Akademie-Verlag, 1953).
  • L. Landau and E. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Oxford, Pergamon Press, 1981).
  • M.J. Duff, B.E.W. Nilsson, and C.N. Pope, Physics Reports 130, 1 (1986).
  • N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. Lett. B 429, 263 (1998).
  • N.V. Krasnikov and V.A. Matveev, Physics-Uspekhi 47, 643 (2004).
  • R.C. Myers and M.J. Perry. Ann. Phys. 172, 304 (1986).
  • S. Flugge. Practical quantum mechanics I (Berlin-Heidelberg-NY, Springer-Verlag, 1971).
  • Th. Appelquist, A. Chodos, and P.G.O. Ereund (eds.). Modern Kaluza-Klein theories (Menlo Park, Addison-Wesley, 1987).
  • V.A. Rubakov, Physics-Uspekhi 44, 871 (2001).

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  • Bound States in the Compactified Gravity

Abstract Views: 120  |  PDF Views: 22

Authors

Askold Duviryak
Institute for Condensed Matter Physics, The National Academy of Sciences of Ukraine, Lviv, Ukraine

Abstract


A potential of pointlike mass in the partially compactified multidimensional space is considered. The problem is reduced to the multidimensional Poisson equation with the Dirac comb source in r.h.s. Explicit solutions are built in the cases of 2D and 4D spaces with one compact dimension. The last example of the potential is used in the Schrodinger equation. Bound states of a gravitating test particle on 3D brane of 4D compactified space are studied by means of various approximate methods.

Keywords


Gravitation, Compactification, Schrodinger Equation, Bound States.

References