Abstract
A relation between two exactly-solvable problems on a circle namely singular Coulomb and singular oscillator systems is established within the phase space path integral formalism via the delta functional method. It is shown that, by using a coordinate transformation the path integral for the one-dimensional singular Coulomb problem coincides to the onedimensional singular oscillator path integral to involve Pöschl-Teller-type path integral representation. The result of the singular oscillator problem is used to construct the energy spectrum and wave functions for singular Coulomb potential, exploiting the close correspondence that exists between the two systems.
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