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Estimation of Boron Ground State Energy by Monte Carlo Simulation

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), 2015. Published by Science Publishing Group

Keywords

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

References
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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}
    }
    

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    T1  - Estimation of Boron Ground State Energy by Monte Carlo Simulation
    AU  - K. M. Ariful Kabir
    AU  - Amal Halder
    Y1  - 2015/05/06
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    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
  • Department Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

  • Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

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