Study of the Lennard-Jones and H₂ potentials in the framework of the Morse based algebraic DVR approach

Abstract

We propose a method based on an algebraic discrete variable representation (DVR) of the coordinate and momentum in the scheme of complete basis related to the 1D Morse potential, with this approach, a Hamiltonian associated to a 1D system can be expressed in terms of diagonal matrices using the transformation coefficients and the diagonalization of the matrix representation of the coordinate and momentum. We probe the scope of our method obtaining the solutions associated of the Lennard-Jones potential, also we apply the method to a practical example considering the ab initio potential of the H2 molecule. For both cases, the vibrational energies and the wave functions were obtained with good accuracy and low computational cost.