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Band Calculation of 2D Square Lattice Using the Method of Successive Over-Relaxation

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Advances in Computer, Communication and Control

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 41))

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Abstract

Successive over-relaxation method has been adopted to find the wave functions corresponding to the band states and surface states and also to solve energy dispersion relation for 2D finite crystal of desirable shape and size with periodic and non-periodic potentials. This method enables us to study the finite size effect in 2D crystals without costing too much computer time like ab initio methods. The major advantage of over-relaxation method is its simplicity as well as its usefulness in both lower and higher dimensional finite systems.

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References

  1. Bhattacharya, P.: Semiconductor Optoelectronic Devices, 2nd ed. Pearson Education (1997)

    Google Scholar 

  2. Streetman, B.G., Banerjee, S.K.: Solid State Electronic Devices, 6th ed. Pearson Education (2006)

    Google Scholar 

  3. McLachlan, N.W.: Theory and Application of Mathieu Functions, 1st ed. Oxford (1947)

    Google Scholar 

  4. Inglesfield, J.E.: Surface electronic structure. IOP Sci. Rep. Prog. Phys. 45 (1982)

    Article  Google Scholar 

  5. Callaway, J.: Energy Band Theory. Academic Press, New York and London (1964)

    Book  Google Scholar 

  6. Kittel, C.: Introduction to Solid State Physics, 8th ed. Wiley (2005)

    Google Scholar 

  7. Chow, P.C.: Computer solutions to the Schrödinger equation. Am. J. Phys. 40, 730734 (1972)

    Article  Google Scholar 

  8. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in Fortran 77, The Art of Scientific Computing. 2nd ed. Cambridge University Press (1992)

    Google Scholar 

  9. Pillai, M., Goglio, J., Walker, Thad G.: Matrix numerov method for solving Schrödinger’s equation. Am. J. Phys. 80, 1017 (2012)

    Article  Google Scholar 

  10. Parr, R.G.: Density functional theory. Ann. Rev. Phys. Chem. 34, 631–656 (1983)

    Article  Google Scholar 

  11. Schmid, E.W., Spitz, G., Lösch, W.: Theoretical Physics on the personal Computer. Springer (1987)

    Google Scholar 

  12. Daniel, V.: Schroeder: the variational-relaxation algorithm for finding quantum bound states. Am. J. Phys. 85, 698 (2017)

    Article  Google Scholar 

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Acknowledgements

Shayari Basu is grateful to DST, Govt. of India for INSPIRE Fellowship.

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Authors and Affiliations

  1. Department of Physics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India

    Shayari Basu & Syed Minhaz Hossain

Authors
  1. Shayari Basu
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  2. Syed Minhaz Hossain
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Corresponding author

Correspondence to Shayari Basu .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Kalyani, Kalyani, West Bengal, India

    Utpal Biswas

  2. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Amit Banerjee

  3. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, India

    Sukhomay Pal

  4. Department of Electronics and Communication Engineering, Asansol Engineering College, Asansol, West Bengal, India

    Arindam Biswas

  5. Department of Mechanical Engineering, Asansol Engineering College, Asansol, West Bengal, India

    Debashis Sarkar

  6. Department of Physics, Asansol Engineering College, Asansol, West Bengal, India

    Sandip Haldar

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Basu, S., Hossain, S.M. (2019). Band Calculation of 2D Square Lattice Using the Method of Successive Over-Relaxation. In: Biswas, U., Banerjee, A., Pal, S., Biswas, A., Sarkar, D., Haldar, S. (eds) Advances in Computer, Communication and Control. Lecture Notes in Networks and Systems, vol 41. Springer, Singapore. https://doi.org/10.1007/978-981-13-3122-0_36

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  • DOI: https://doi.org/10.1007/978-981-13-3122-0_36

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-3121-3

  • Online ISBN: 978-981-13-3122-0

  • eBook Packages: EngineeringEngineering (R0)

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