SUMMING THE SPECTRAL REPRESENTATIONS OF POSCHL-TELLER AND ROSEN-MORSE FIXED-ENERGY AMPLITUDES

The spectral representations of the fixed-energy amplitude of the symmetric and the general Poschl-Teller potentials are summed via a Sommerfeld-Watson transformation which leads to a simple closed-form expression. The result is used to write down a similar expression for the symmetric and general Rosen-Morse potentials, exploiting the close correspondence that exists between the two systems within the Schrodinger theory and the path integral formalism via a Duru-Kleinert transformation. From the singularities of the latter amplitude the bound and continuum states of the general Rosen-Morse potential are extracted.