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

Leidy Y. Medina, Francisco Núñez-Zarur, Jhon F. Pérez-Torres

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1 Scopus citations

Abstract

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 Schrödinger equation. In order to solve the fractional Schrödinger 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 Schrödinger 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 Schrödinger equation. Finally, the probability and flux distributions are presented, demonstrating the applicability of the fractional Schrödinger equation for taking into account nonadiabatic effects.

Original languageEnglish
Article numbere25952
JournalInternational Journal of Quantum Chemistry
Volume119
Issue number16
DOIs
StatePublished - 1 Jan 2019

Keywords

  • Fourier grid Hamiltonian method
  • fractional Schrödinger equation
  • nonadiabatic effects

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