J L A Coelho and R L P G Amaral 2002 J. Phys. A: Math. Gen. 35 5255 doi:10.1088/0305-4470/35/25/307
J L A Coelho and R L P G Amaral
Show affiliationsThe Schrödinger equations for the Coulomb and the harmonic oscillator potentials are solved in the cosmic string conical spacetime. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunction is performed through the introduction of non-local ladder operators. By exploring the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues for the angular momentum operators in three dimensions are reproduced. A generalization for N dimensions is performed for both Coulomb and harmonic oscillator problems in angular deficit spacetimes. The connection among the states and energies of both problems in these topologically non-trivial spacetimes is thus established.
83E30 String and superstring theories (See also 81T30)
81T30 String and superstring theories; other extended objects (e.g., branes) (See also 83E30)
Issue 25 (28 June 2002)
Received 4 December 2001, in final form 11 April 2002
Published 14 June 2002
J L A Coelho and R L P G Amaral 2002 J. Phys. A: Math. Gen. 35 5255
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