Estimation of Boron Ground State Energy by Monte Carlo Simulation

K. M. Ariful Kabir; Amal Halder

doi:doi:10.11648/j.ajam.20150303.15

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Estimation of Boron Ground State Energy by Monte Carlo Simulation

K. M. Ariful Kabir, Amal Halder

Published in American Journal of Applied Mathematics (Volume 3, Issue 3)

Received: 2 April 2015 Accepted: 23 April 2015 Published: 6 May 2015

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Abstract

Quantum Monte Carlo (QMC) method is a powerful computational tool for finding accurate approximation solutions of the quantum many body stationary Schrödinger equations for atoms, molecules, solids and a variety of model systems. Using Variational Monte Carlo method we have calculated the ground state energy of the Boron atom. Our calculations are based on using a modified five parameters trial wave function which leads to good result comparing with fewer parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Boron. Based on comparisons, the energy obtained in our simulation are in excellent agreement with experimental and other well established values.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 3)
DOI	10.11648/j.ajam.20150303.15
Page(s)	106-111
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

Monte Carlo Simulation, Boron, Ground State Energy, Schrödinger Equation

References

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K. M. Ariful Kabir, Amal Halder. (2015). Estimation of Boron Ground State Energy by Monte Carlo Simulation. American Journal of Applied Mathematics, 3(3), 106-111. https://doi.org/10.11648/j.ajam.20150303.15

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ACS Style

K. M. Ariful Kabir; Amal Halder. Estimation of Boron Ground State Energy by Monte Carlo Simulation. Am. J. Appl. Math. 2015, 3(3), 106-111. doi: 10.11648/j.ajam.20150303.15

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AMA Style

K. M. Ariful Kabir, Amal Halder. Estimation of Boron Ground State Energy by Monte Carlo Simulation. Am J Appl Math. 2015;3(3):106-111. doi: 10.11648/j.ajam.20150303.15

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@article{10.11648/j.ajam.20150303.15,
  author = {K. M. Ariful Kabir and Amal Halder},
  title = {Estimation of Boron Ground State Energy by Monte Carlo Simulation},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {106-111},
  doi = {10.11648/j.ajam.20150303.15},
  url = {https://doi.org/10.11648/j.ajam.20150303.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.15},
  abstract = {Quantum Monte Carlo (QMC) method is a powerful computational tool for finding accurate approximation solutions of the quantum many body stationary Schrödinger equations for atoms, molecules, solids and a variety of model systems. Using Variational Monte Carlo method we have calculated the ground state energy of the Boron atom. Our calculations are based on using a modified five parameters trial wave function which leads to good result comparing with fewer parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Boron. Based on comparisons, the energy obtained in our simulation are in excellent agreement with experimental and other well established values.},
 year = {2015}
}

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TY  - JOUR
T1  - Estimation of Boron Ground State Energy by Monte Carlo Simulation
AU  - K. M. Ariful Kabir
AU  - Amal Halder
Y1  - 2015/05/06
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150303.15
DO  - 10.11648/j.ajam.20150303.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 106
EP  - 111
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150303.15
AB  - Quantum Monte Carlo (QMC) method is a powerful computational tool for finding accurate approximation solutions of the quantum many body stationary Schrödinger equations for atoms, molecules, solids and a variety of model systems. Using Variational Monte Carlo method we have calculated the ground state energy of the Boron atom. Our calculations are based on using a modified five parameters trial wave function which leads to good result comparing with fewer parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Boron. Based on comparisons, the energy obtained in our simulation are in excellent agreement with experimental and other well established values.
VL  - 3
IS  - 3
ER  -

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Author Information

K. M. Ariful Kabir

Department Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
Amal Halder

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

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APA Style

K. M. Ariful Kabir, Amal Halder. (2015). Estimation of Boron Ground State Energy by Monte Carlo Simulation. American Journal of Applied Mathematics, 3(3), 106-111. https://doi.org/10.11648/j.ajam.20150303.15

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ACS Style

K. M. Ariful Kabir; Amal Halder. Estimation of Boron Ground State Energy by Monte Carlo Simulation. Am. J. Appl. Math. 2015, 3(3), 106-111. doi: 10.11648/j.ajam.20150303.15

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AMA Style

K. M. Ariful Kabir, Amal Halder. Estimation of Boron Ground State Energy by Monte Carlo Simulation. Am J Appl Math. 2015;3(3):106-111. doi: 10.11648/j.ajam.20150303.15

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@article{10.11648/j.ajam.20150303.15,
  author = {K. M. Ariful Kabir and Amal Halder},
  title = {Estimation of Boron Ground State Energy by Monte Carlo Simulation},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {106-111},
  doi = {10.11648/j.ajam.20150303.15},
  url = {https://doi.org/10.11648/j.ajam.20150303.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.15},
  abstract = {Quantum Monte Carlo (QMC) method is a powerful computational tool for finding accurate approximation solutions of the quantum many body stationary Schrödinger equations for atoms, molecules, solids and a variety of model systems. Using Variational Monte Carlo method we have calculated the ground state energy of the Boron atom. Our calculations are based on using a modified five parameters trial wave function which leads to good result comparing with fewer parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Boron. Based on comparisons, the energy obtained in our simulation are in excellent agreement with experimental and other well established values.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Estimation of Boron Ground State Energy by Monte Carlo Simulation
AU  - K. M. Ariful Kabir
AU  - Amal Halder
Y1  - 2015/05/06
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150303.15
DO  - 10.11648/j.ajam.20150303.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 106
EP  - 111
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150303.15
AB  - Quantum Monte Carlo (QMC) method is a powerful computational tool for finding accurate approximation solutions of the quantum many body stationary Schrödinger equations for atoms, molecules, solids and a variety of model systems. Using Variational Monte Carlo method we have calculated the ground state energy of the Boron atom. Our calculations are based on using a modified five parameters trial wave function which leads to good result comparing with fewer parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Boron. Based on comparisons, the energy obtained in our simulation are in excellent agreement with experimental and other well established values.
VL  - 3
IS  - 3
ER  -

Copy | Download