Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms

Salah Badawi Doma; Nazih Abdelhamid Elnohy; Mahmoud Ahmed Salem

doi:doi:10.11648/j.ijhep.20190602.13

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Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem

Published in International Journal of High Energy Physics (Volume 6, Issue 2)

Received: 7 November 2019 Accepted: 28 November 2019 Published: 24 December 2019

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Abstract

The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li⁺, and Be²⁺ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.

Published in	International Journal of High Energy Physics (Volume 6, Issue 2)
DOI	10.11648/j.ijhep.20190602.13
Page(s)	42-53
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Variational Monte Carlo Method, Correlation Functions, Helium Like Ions, Helium Excited States, Confined Helium, Strong Magnetic Field

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Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem. (2019). Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. International Journal of High Energy Physics, 6(2), 42-53. https://doi.org/10.11648/j.ijhep.20190602.13

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ACS Style

Salah Badawi Doma; Nazih Abdelhamid Elnohy; Mahmoud Ahmed Salem. Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. Int. J. High Energy Phys. 2019, 6(2), 42-53. doi: 10.11648/j.ijhep.20190602.13

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AMA Style

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem. Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. Int J High Energy Phys. 2019;6(2):42-53. doi: 10.11648/j.ijhep.20190602.13

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@article{10.11648/j.ijhep.20190602.13,
  author = {Salah Badawi Doma and Nazih Abdelhamid Elnohy and Mahmoud Ahmed Salem},
  title = {Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms},
  journal = {International Journal of High Energy Physics},
  volume = {6},
  number = {2},
  pages = {42-53},
  doi = {10.11648/j.ijhep.20190602.13},
  url = {https://doi.org/10.11648/j.ijhep.20190602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20190602.13},
  abstract = {The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.},
 year = {2019}
}

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TY  - JOUR
T1  - Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms
AU  - Salah Badawi Doma
AU  - Nazih Abdelhamid Elnohy
AU  - Mahmoud Ahmed Salem
Y1  - 2019/12/24
PY  - 2019
N1  - https://doi.org/10.11648/j.ijhep.20190602.13
DO  - 10.11648/j.ijhep.20190602.13
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 42
EP  - 53
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20190602.13
AB  - The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.
VL  - 6
IS  - 2
ER  -

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Author Information

Salah Badawi Doma

Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
Nazih Abdelhamid Elnohy

Department of Physics, Faculty of Science, Alexandria University, Alexandria, Egypt
Mahmoud Ahmed Salem

Department of Physics, Faculty of Science, Alexandria University, Alexandria, Egypt

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APA Style

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem. (2019). Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. International Journal of High Energy Physics, 6(2), 42-53. https://doi.org/10.11648/j.ijhep.20190602.13

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ACS Style

Salah Badawi Doma; Nazih Abdelhamid Elnohy; Mahmoud Ahmed Salem. Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. Int. J. High Energy Phys. 2019, 6(2), 42-53. doi: 10.11648/j.ijhep.20190602.13

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AMA Style

Salah Badawi Doma, Nazih Abdelhamid Elnohy, Mahmoud Ahmed Salem. Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms. Int J High Energy Phys. 2019;6(2):42-53. doi: 10.11648/j.ijhep.20190602.13

Copy | Download

@article{10.11648/j.ijhep.20190602.13,
  author = {Salah Badawi Doma and Nazih Abdelhamid Elnohy and Mahmoud Ahmed Salem},
  title = {Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms},
  journal = {International Journal of High Energy Physics},
  volume = {6},
  number = {2},
  pages = {42-53},
  doi = {10.11648/j.ijhep.20190602.13},
  url = {https://doi.org/10.11648/j.ijhep.20190602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20190602.13},
  abstract = {The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms
AU  - Salah Badawi Doma
AU  - Nazih Abdelhamid Elnohy
AU  - Mahmoud Ahmed Salem
Y1  - 2019/12/24
PY  - 2019
N1  - https://doi.org/10.11648/j.ijhep.20190602.13
DO  - 10.11648/j.ijhep.20190602.13
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 42
EP  - 53
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20190602.13
AB  - The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li+, and Be2+ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.
VL  - 6
IS  - 2
ER  -

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