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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 \((V_{2}\rightarrow -V_{2},q=1)\) and the radial Eckart potential \((V_{1}\rightarrow -V_{1},q=1)\) are also briefly discussed.

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