Energetics and stability of discrete charge distribution on the surface of a sphere

Oymak, H
Erkoç, Şakir
We have investigated the minimum-energy distribution of N, 3 ≤ N ≤ 97, equal point charges confined to the surface of a sphere. Charges interact with each other via the Coulomb potential of the form 1/r. Minimum-energy distributions have been determined by minimizing the tangential forces on each charge. Further numerical evidence shows that in the minimum-energy state of N charges on the sphere, it is not possible to place a charge at the geometrical center. Besides, it has been found that the most and reliable information about the relative stability properties of the distributions can be obtained with the help of second difference energy consideration.


Distribution of point charges on a thin conducting disk
Oymak, H; Erkoç, Şakir (World Scientific Pub Co Pte Lt, 2000-07-01)
We investigate the minimum energy configuration of N equal point charges interacting via the Coulomb potential 1/r, and placed on an infinitely thin conducting disk. By minimizing total interaction Energy, we obtain numerically the minimum energy configurations from which the rules for the distribution of charges on the disk are obtained.
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2008-09-01)
We present the exact solution of the Klein Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov-Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular ...
Exact solutions of the modified Kratzer potential plus ring-shaped potential in the d-dimensional Schrodinger equation by the Nikiforov-Uvarov method
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2008-02-01)
We present analytically the exact energy bound-states solutions of the Schrodinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov-Uvarov method. We obtain an explicit solution of the wave functions in terms of hyper-geometric functions (Laguerre polynomials). The results obtained in this work are more general and true for any dimension which can be reduced to the well-known three-dimensional forms given by other works.
Bound states of the Klein-Gordon equation for Woods-Saxon potential with position dependent mass
Arda, Altug; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2008-05-01)
The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.
Gardner's deformations of the Boussinesq equations
Karasu, Atalay (IOP Publishing, 2006-09-15)
Using the algebraic method of Gardner's deformations for completely integrable systems, we construct recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri schemes for these equations, we obtain new integrable systems adjoint with respect to the initial ones and describe their Hamiltonian structures and symmetry properties.
Citation Formats
H. Oymak and Ş. Erkoç, “Energetics and stability of discrete charge distribution on the surface of a sphere,” INTERNATIONAL JOURNAL OF MODERN PHYSICS C, pp. 293–305, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52114.