Semiclassical calculation of a radial path integral

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Abstract
A semiclassical method of evaluating a path integral for the central potential problem is presented. The Langer transformation r=ex, when applied properly to a radial path integral, brings about an appropriate range of integration and the desired angular momentum modification (l(l+1))1/2ℏ→(l+1/2)ℏ. The resultant path integral becomes assessable by semiclassical calculations. The method is seen to work for obtaining the exact energy spectra of the isotropic harmonic oscillator and the hydrogen atom bound states.