Conditionally solvable path integral problems. (English) Zbl 0872.58016
Summary: 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.
MSC:
58D30 | Applications of manifolds of mappings to the sciences |
81S40 | Path integrals in quantum mechanics |
34L30 | Nonlinear ordinary differential operators |