Path integral solution for a Klein-Gordon particle in vector and scalar deformed radial Rosen-Morse-type potentials

Abstract

The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's function associated with different shapes of the potentials. For $q\le -1$, and $\frac{1}{2\alpha }\ln \left|q\right|<r<+\infty$, the energy equation and the corresponding wave functions are deduced for the $l$ states using an appropriate approximation to the centrifugal potential term. When $-1<q<0$ or $q>0$, it is shown that the quantization conditions for the bound state energy levels $E_{n_r}$ are transcendental equations which can be solved numerically. Three special cases such as the standard radial Manning-Rosen potential $(\left|q\right|=1)$, the standard radial Rosen-Morse potential and the radial Eckart potential are also briefly discussed.

16 pages

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