A relativistic model of the $N$-dimensional singular oscillator

Details A relativistic model of the $N$-dimensional singular oscillator A relativistic model of the $N$-dimensional singular oscillator

2006-12-05

arxiv.org/abs/math-ph/0612015v1

J.Phys. A40 (2007) 289-295

Physics

Mathematical Physics

8 pages, accepted for publication in J. Phys. A

Scientific paper

10.1088/1751-8113/40/2/008

Exactly solvable $N$-dimensional model of the quantum isotropic singular oscillator in the relativistic configurational $\vec r_N$-space is proposed. It is shown that through the simple substitutions the finite-difference equation for the $N$-dimensional singular oscillator can be reduced to the similar finite-difference equation for the relativistic isotropic three-dimensional singular oscillator. We have found the radial wavefunctions and energy spectrum of the problem and constructed a dynamical symmetry algebra.

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