Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrodinger equation

摘要

Nonadiabatic effects in the nuclear dynamics of the H-2(+) molecular ion, initiated by ionization of the H-2 molecule, is studied by means of the probability and flux distribution functions arising from the space fractional Schrodinger equation. In order to solve the fractional Schrodinger eigenvalue equation, it is shown that the quantum Riesz fractional derivative operator fulfills the usual properties of the quantum momentum operator acting on the bra and ket vectors of the abstract Hilbert space. Then, the fractional Fourier grid Hamiltonian method is implemented and applied to molecular vibrations. The eigenenergies and eigenfunctions of the fractional Schrodinger equation describing the vibrational motion of the H-2(+) and D-2(+) molecules are analyzed. In particular, it is shown that the position-momentum Heisenberg's uncertainty relationship holds independently of the fractional Schrodinger equation. Finally, the probability and flux distributions are presented, demonstrating the applicability of the fractional Schrodinger equation for taking into account nonadiabatic effects.