Premium
Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
Author(s) -
Medina Leidy Y.,
NúñezZarur Francisco,
PérezTorres Jhon F.
Publication year - 2019
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25952
Subject(s) - schrödinger equation , eigenfunction , hamiltonian (control theory) , physics , fractional calculus , mathematical physics , quantum mechanics , operator (biology) , wave function , position and momentum space , eigenvalues and eigenvectors , mathematics , chemistry , mathematical optimization , biochemistry , repressor , transcription factor , gene
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.