Effective potentials and the Gel''fand—Levitan equation
Authors:
Nimrod Moiseyev
Affiliation:
Department of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel
Department of Quantum Chemistry, Uppsala University, Box 518, 751 20 Uppsala, Sweden
Abstract:
Moses et al, have derived an algorithm using the Gel'fand-Levitan equation for generating exactly solvable potentials for a particle in a box, harmonic oscillator, and Coulomb potentials by adding or subtracting a finite number of eigenvalues. We propose that their algorithm can be used to evaluate effective potentials for non exactly soluble molecular model Hamiltonians. We show that the algorithm can be used to remove bound states from the spectrum and to obtain an effective potential which supports predissociation resonances only. It can also be used to remove a specific resonance state from the spectrum, and to facilitate evaluations of excited states.