Manning-Rosen Potential Research Articles

Conditionally solvable path integral problems

Some specific conditionally exactly solvable potentials are discussed within the path integral formalism. They generalize the usually known potentials by the incorporation of fractional power behaviour and strongly anharmonic terms. We find four different kinds of such potential: the first is related to the Coulomb potential, the second is an anharmonic confinement potential, and the third and fourth are related to the Manning-Rosen potential.

Comment on "Four-parameter exactly solvable potential for diatomic molecules"

This Comment precludes any chance of discovering a new potential that would allow one to solve the one-dimensional Schr\"odinger equation in terms of hypergeometric functions. In particular, it argues that the potential function suggested by Hua [Phys. Rev. A 42, 2524 (1990)] is the well-known Tietz potential, which in turn is a combination of the Rosen-Morse, Morse, and Manning-Rosen potentials presented in a common form.

The path integral for the Kepler problem on the pseudosphere

The path integral for the generalized Kepler problem on the pseudosphere is calculated. As the generalized Kepler problem we describe the potential problem V(α) = −(Ze2R)(cothα−1) (α>0, R-curvature) on the D-dimensional pseudosphere, whereas for the genuine Kepler problem this feature of the potential is only true for the four-dimensional pseudosphere. Energy spectrum and wave-functions are explicitly calculated. The result is compared with the flat-space limit (i.e., R → ∞) and with the free motion on the pseudosphere. The application of the result of the path integral solution of the Manning-Rosen potential plays a crucial role in the calculation.