Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle

Md Moniruzzaman; Md Nasir Uddin; Syed Bodiuzzaman Faruque

doi:doi:10.11648/j.ijhep.20220902.11

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Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle

Md Moniruzzaman, Md Nasir Uddin, Syed Bodiuzzaman Faruque

Published in International Journal of High Energy Physics (Volume 9, Issue 2)

Received: 30 May 2022 Accepted: 29 July 2022 Published: 9 August 2022

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Abstract

There is no minimal uncertainty in position measurement in the Heisenberg uncertainty principle is to be considered as the minimum of space resolution, whereas numerous theories of quantum gravity predict the existence of a lower bound to the possible resolution of distances. The minimal length is considered commonly by a modification of the Heisenberg uncertainty principle into the generalized uncertainty principle (GUP). The application of GUP modifies every equation of motion of quantum mechanics and consequently, a new window of research has opened to study quantum mechanical problems under the framework of GUP. In this article, we present an exact solution of the Dirac equation with a combined static electric and magnetic field under the framework of GUP and obtain exact energy spectrums. The spectrums manifest a super-symmetry for the sufficient large magnetic field intensity compared to the electric field intensity. The methodology of the solution is designed for convenient implementation of the key property of the harmonic oscillator, the kinetic and potential energy parts of the Hamiltonian are of equal weight. An obligation for the existence of the solution is found that the magnetic field is stronger than the electric field. Our obtained result is confirmed by rendering energy levels of a relativistic electron in an external normal magnetic field, found in the literature.

Published in	International Journal of High Energy Physics (Volume 9, Issue 2)
DOI	10.11648/j.ijhep.20220902.11
Page(s)	25-35
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

Dirac Equation, Static Electric Field, Static Magnetic Field, Generalized Uncertainty Principle

References

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APA Style

Md Moniruzzaman, Md Nasir Uddin, Syed Bodiuzzaman Faruque. (2022). Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle. International Journal of High Energy Physics, 9(2), 25-35. https://doi.org/10.11648/j.ijhep.20220902.11

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ACS Style

Md Moniruzzaman; Md Nasir Uddin; Syed Bodiuzzaman Faruque. Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle. Int. J. High Energy Phys. 2022, 9(2), 25-35. doi: 10.11648/j.ijhep.20220902.11

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AMA Style

Md Moniruzzaman, Md Nasir Uddin, Syed Bodiuzzaman Faruque. Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle. Int J High Energy Phys. 2022;9(2):25-35. doi: 10.11648/j.ijhep.20220902.11

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@article{10.11648/j.ijhep.20220902.11,
  author = {Md Moniruzzaman and Md Nasir Uddin and Syed Bodiuzzaman Faruque},
  title = {Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle},
  journal = {International Journal of High Energy Physics},
  volume = {9},
  number = {2},
  pages = {25-35},
  doi = {10.11648/j.ijhep.20220902.11},
  url = {https://doi.org/10.11648/j.ijhep.20220902.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20220902.11},
  abstract = {There is no minimal uncertainty in position measurement in the Heisenberg uncertainty principle is to be considered as the minimum of space resolution, whereas numerous theories of quantum gravity predict the existence of a lower bound to the possible resolution of distances. The minimal length is considered commonly by a modification of the Heisenberg uncertainty principle into the generalized uncertainty principle (GUP). The application of GUP modifies every equation of motion of quantum mechanics and consequently, a new window of research has opened to study quantum mechanical problems under the framework of GUP. In this article, we present an exact solution of the Dirac equation with a combined static electric and magnetic field under the framework of GUP and obtain exact energy spectrums. The spectrums manifest a super-symmetry for the sufficient large magnetic field intensity compared to the electric field intensity. The methodology of the solution is designed for convenient implementation of the key property of the harmonic oscillator, the kinetic and potential energy parts of the Hamiltonian are of equal weight. An obligation for the existence of the solution is found that the magnetic field is stronger than the electric field. Our obtained result is confirmed by rendering energy levels of a relativistic electron in an external normal magnetic field, found in the literature.},
 year = {2022}
}

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TY  - JOUR
T1  - Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle
AU  - Md Moniruzzaman
AU  - Md Nasir Uddin
AU  - Syed Bodiuzzaman Faruque
Y1  - 2022/08/09
PY  - 2022
N1  - https://doi.org/10.11648/j.ijhep.20220902.11
DO  - 10.11648/j.ijhep.20220902.11
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 25
EP  - 35
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20220902.11
AB  - There is no minimal uncertainty in position measurement in the Heisenberg uncertainty principle is to be considered as the minimum of space resolution, whereas numerous theories of quantum gravity predict the existence of a lower bound to the possible resolution of distances. The minimal length is considered commonly by a modification of the Heisenberg uncertainty principle into the generalized uncertainty principle (GUP). The application of GUP modifies every equation of motion of quantum mechanics and consequently, a new window of research has opened to study quantum mechanical problems under the framework of GUP. In this article, we present an exact solution of the Dirac equation with a combined static electric and magnetic field under the framework of GUP and obtain exact energy spectrums. The spectrums manifest a super-symmetry for the sufficient large magnetic field intensity compared to the electric field intensity. The methodology of the solution is designed for convenient implementation of the key property of the harmonic oscillator, the kinetic and potential energy parts of the Hamiltonian are of equal weight. An obligation for the existence of the solution is found that the magnetic field is stronger than the electric field. Our obtained result is confirmed by rendering energy levels of a relativistic electron in an external normal magnetic field, found in the literature.
VL  - 9
IS  - 2
ER  -

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Author Information

Md Moniruzzaman

Department of Physics, Mawlana Bhashani Science & Technology University, Tangail, Bangladesh
Md Nasir Uddin

Department of Physics, Mawlana Bhashani Science & Technology University, Tangail, Bangladesh
Syed Bodiuzzaman Faruque

Department of Physics, Shahjalal University of Science & Technology, Sylhet, Bangladesh

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APA Style

Md Moniruzzaman, Md Nasir Uddin, Syed Bodiuzzaman Faruque. (2022). Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle. International Journal of High Energy Physics, 9(2), 25-35. https://doi.org/10.11648/j.ijhep.20220902.11

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ACS Style

Md Moniruzzaman; Md Nasir Uddin; Syed Bodiuzzaman Faruque. Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle. Int. J. High Energy Phys. 2022, 9(2), 25-35. doi: 10.11648/j.ijhep.20220902.11

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AMA Style

Md Moniruzzaman, Md Nasir Uddin, Syed Bodiuzzaman Faruque. Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle. Int J High Energy Phys. 2022;9(2):25-35. doi: 10.11648/j.ijhep.20220902.11

Copy | Download

@article{10.11648/j.ijhep.20220902.11,
  author = {Md Moniruzzaman and Md Nasir Uddin and Syed Bodiuzzaman Faruque},
  title = {Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle},
  journal = {International Journal of High Energy Physics},
  volume = {9},
  number = {2},
  pages = {25-35},
  doi = {10.11648/j.ijhep.20220902.11},
  url = {https://doi.org/10.11648/j.ijhep.20220902.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20220902.11},
  abstract = {There is no minimal uncertainty in position measurement in the Heisenberg uncertainty principle is to be considered as the minimum of space resolution, whereas numerous theories of quantum gravity predict the existence of a lower bound to the possible resolution of distances. The minimal length is considered commonly by a modification of the Heisenberg uncertainty principle into the generalized uncertainty principle (GUP). The application of GUP modifies every equation of motion of quantum mechanics and consequently, a new window of research has opened to study quantum mechanical problems under the framework of GUP. In this article, we present an exact solution of the Dirac equation with a combined static electric and magnetic field under the framework of GUP and obtain exact energy spectrums. The spectrums manifest a super-symmetry for the sufficient large magnetic field intensity compared to the electric field intensity. The methodology of the solution is designed for convenient implementation of the key property of the harmonic oscillator, the kinetic and potential energy parts of the Hamiltonian are of equal weight. An obligation for the existence of the solution is found that the magnetic field is stronger than the electric field. Our obtained result is confirmed by rendering energy levels of a relativistic electron in an external normal magnetic field, found in the literature.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Exact Solution of the Dirac Equation with a Combined Static Electric and Magnetic Field in the Context of Generalized Uncertainty Principle
AU  - Md Moniruzzaman
AU  - Md Nasir Uddin
AU  - Syed Bodiuzzaman Faruque
Y1  - 2022/08/09
PY  - 2022
N1  - https://doi.org/10.11648/j.ijhep.20220902.11
DO  - 10.11648/j.ijhep.20220902.11
T2  - International Journal of High Energy Physics
JF  - International Journal of High Energy Physics
JO  - International Journal of High Energy Physics
SP  - 25
EP  - 35
PB  - Science Publishing Group
SN  - 2376-7448
UR  - https://doi.org/10.11648/j.ijhep.20220902.11
AB  - There is no minimal uncertainty in position measurement in the Heisenberg uncertainty principle is to be considered as the minimum of space resolution, whereas numerous theories of quantum gravity predict the existence of a lower bound to the possible resolution of distances. The minimal length is considered commonly by a modification of the Heisenberg uncertainty principle into the generalized uncertainty principle (GUP). The application of GUP modifies every equation of motion of quantum mechanics and consequently, a new window of research has opened to study quantum mechanical problems under the framework of GUP. In this article, we present an exact solution of the Dirac equation with a combined static electric and magnetic field under the framework of GUP and obtain exact energy spectrums. The spectrums manifest a super-symmetry for the sufficient large magnetic field intensity compared to the electric field intensity. The methodology of the solution is designed for convenient implementation of the key property of the harmonic oscillator, the kinetic and potential energy parts of the Hamiltonian are of equal weight. An obligation for the existence of the solution is found that the magnetic field is stronger than the electric field. Our obtained result is confirmed by rendering energy levels of a relativistic electron in an external normal magnetic field, found in the literature.
VL  - 9
IS  - 2
ER  -

Copy | Download