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

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

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

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 originalInglés
Número de artículoe25952
PublicaciónInternational Journal of Quantum Chemistry
Volumen119
N.º16
DOI
EstadoPublicada - 1 ene 2019

Huella dactilar

Momentum
flux density
Molecular vibrations
Fluxes
Hamiltonians
Molecules
Hilbert spaces
Eigenvalues and eigenfunctions
Ionization
Distribution functions
Ions
Derivatives
momentum
operators
Hilbert space
molecular ions
molecules
eigenvectors
eigenvalues
distribution functions

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title = "Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schr{\"o}dinger equation",
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 Schr{\"o}dinger equation. In order to solve the fractional Schr{\"o}dinger 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 Schr{\"o}dinger 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 Schr{\"o}dinger equation. Finally, the probability and flux distributions are presented, demonstrating the applicability of the fractional Schr{\"o}dinger equation for taking into account nonadiabatic effects.",
keywords = "Fourier grid Hamiltonian method, fractional Schr{\"o}dinger equation, nonadiabatic effects",
author = "Medina, {Leidy Y.} and Francisco N{\'u}{\~n}ez-Zarur and P{\'e}rez-Torres, {Jhon F.}",
year = "2019",
month = "1",
day = "1",
doi = "10.1002/qua.25952",
language = "Ingl{\'e}s",
volume = "119",
journal = "International Journal of Quantum Chemistry",
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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.

En: International Journal of Quantum Chemistry, Vol. 119, N.º 16, e25952, 01.01.2019.

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión 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

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U2 - 10.1002/qua.25952

DO - 10.1002/qua.25952

M3 - Artículo

VL - 119

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

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M1 - e25952

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