16 research outputs found
Path integral for relativistic oscillators: model of the Klein-Gordon particle in AdS space
Explicit path integration is carried out for the Green's functions of special
relativistic harmonic oscillators in (1+1)- and (3+1)-dimensional Minkowski
space-time modeled by a Klein-Gordon particle in the universal covering
space-time of the anti-de Sitter static space-time. The energy spectrum
together with the normalized wave functions are obtained. In the
non-relativistic limit, the bound states of the one- and three-dimensional
ordinary oscillators are regained.Comment: 23 pages, no figures. Accepted for publication in Eur.Phys.J.
Algebraic treatment of the confluent Natanzon potentials
Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas,
the Green's function for the class of the confluent Natanzon potentials is
constructed straightforwardly. The bound-state energy spectrum is then
determined. Eventually, the three-dimensional harmonic potential, the
three-dimensional Coulomb potential and the Morse potential may all be
considered as particular cases.Comment: 9 page