### Resumen

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.

Idioma original | Inglés |
---|---|

Número de artículo | e25952 |

Publicación | International Journal of Quantum Chemistry |

DOI | |

Estado | Publicada - 1 ene 2019 |

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*International Journal of Quantum Chemistry*, [e25952]. https://doi.org/10.1002/qua.25952

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**Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation.** / Medina, Leidy Y.; Núñez-Zarur, Francisco; Pérez-Torres, Jhon F.

Resultado de la investigación: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

TY - JOUR

T1 - Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation

AU - Medina, Leidy Y.

AU - Núñez-Zarur, Francisco

AU - Pérez-Torres, Jhon F.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Fourier grid Hamiltonian method

KW - fractional Schrödinger equation

KW - nonadiabatic effects

UR - http://www.scopus.com/inward/record.url?scp=85064484900&partnerID=8YFLogxK

U2 - 10.1002/qua.25952

DO - 10.1002/qua.25952

M3 - Artículo

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

M1 - e25952

ER -