Manuel Soares

An integral representation for the product of Airy functions

Abstract.An integral representation for the product of Airy functions is given. Particular cases are examined and applications to integrals involving such products are performed.

A quantum method for the inversion of bound - free Franck - Condon factors

An exact quantum method is introduced for the inversion of the bound - free continuum spectrum originating in a single discrete vibrational level. It allows one to obtain an unknown bound-state potential and the transition operator from two observed continuum spectra originating on different vibrational levels of that state and a knowledge of the repulsive final-state potential. This procedure is tested numerically with a couple of well known potentials: an exponential and a Morse potential. A comparison of the exact and the reconstructed potentials is discussed in order to illustrate the numerical limitations of this method.