Calculation of the Average Potential of a Wigner Solid
International Journal of Education, Culture and Society
Volume 3, Issue 3, June 2018, Pages: 49-52
Received: Jun. 24, 2018; Accepted: Jul. 9, 2018; Published: Aug. 8, 2018
Views 1990      Downloads 125
Zhang Yue, College of Physics and Information Science, Hunan Normal University, Changsha, China
Article Tools
Follow on us
The paper corrects a few errors occurring in the calculations of CALLAWAY J on the average potential of a Wigner solid. With respect to the monoatomic bcc and fcc metals, a theory of calculating the average potentials of them is established, and the theoretical results demonstrate that the average potential is directly proportional to the reciprocal of the lattice constant of the crystal. Moreover, the paper performs a great deal of calculations of the average potentials of various bcc and fcc metals, and obtains a lot of numerical results which are valuable for applications.
Wigner Solid, Poisson’s Equation, Average Potential, Lattice Constant
To cite this article
Zhang Yue, Calculation of the Average Potential of a Wigner Solid, International Journal of Education, Culture and Society. Vol. 3, No. 3, 2018, pp. 49-52. doi: 10.11648/j.ijecs.20180303.12
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
HALL G L. Correction to Fuchs’ calculation of the electrostatic energy of a Wigner solid [J]. Phys Rev B, 1979, 19(8): 3921 - 3932.
CALLAWAY J, GLASSER M L. Fourier Coefficients of Crystal Potentials [J]. Phys Rev, 1958, 112(1): 73–77.
HATKE A T, Yang Liu, Engel L W, et al. Microwave spectroscopic observation of a Wigner solid within the 1 / 2 fractional quantum effect [J]. Phys. Rev. B, 2017, 95 (4): 045417.
MONARKHA YURIY. Subharmonic phonon-ripplon coupling in the 2D Wigner solid on superfluid helium [J]. Europhysics Letters, 2017, 118 (6): 67001.
CALLAWAY J. Quantum Theory of the Solid State (Second Edition) [M]. San Diego: Academic Press, INC., 1991:16-19.
REES D G, BEYSENGULOV N R, LIN J J, and KONO K. Stik-Slip Motion of the Wigner Solid on liquid Helium [J]. Phys. Rev. Lett., 2016, 116(20): 206801.
KLEINMAN L. Comment on the average potential of a Wigner solid [J]. Phys Rev B, 1981, 24(12): 7412–7414.
HALL G L. Response to “Comment on the average potential of a Wigner solid” [J]. Phys Rev B, 1981, 24(12): 7415–7418.
BRADBURY T C. Mathematical Methods with Applications to Problems in Physical Sciences [M]. New York: John Wiley & Sons, 1984:109-110.
ASHCROFT N W, MERMIN N D. Solid State Physics [M]. San Francisco: Holt, Rinehart and Winston, 1976.
YOU X Z. Ionic Polarizability [J]. Chinese Science Bulletin, 1974, 19(9):419–423.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186