TIM LaFAVE JR. The Classical Electrostatic Periodic Table, Capacitance of Few Electron Dielectric Spheres, and a Novel Treatment of One- and Two-Electron Finite Quantum Wells

(Under the direction of DR. RAPHAEL TSU)

The centerpiece of this dissertation is the discovery of the classical electrostatic periodic table of elements through non-linear ground state energies coincident with atomic shell-filling resulting from symmetry properties of discrete electrons constrained by a spherically-symmetric system. The time-independent electrostatic equilibrium configuration of few electrons confined to a large classical dielectric sphere is obtained by minimization of the total interaction energy. The interactions model yields more than twice the energy predicted by the classical Gauss model. Each N-electron system is proposed as a unique phase characterized by its symmetry properties. A new monophasic capacitance definition of dielectric spheres is derived from the fundamental relation $Q=CV$. Large differences from the Gauss model are obtained for few-electron systems, but convergence is found in the metallic limit. Of particular significance is the means by which symmetry-dependent properties of atomic-scale devices may be exploited by controlling the internal architecture of charge distributions. This work will be useful to modeling of many-electron chemical and biological systems, such as macromolecules, owing largely to symmetry differences between the Gauss model and the interactions model. The foundation upon which all Nature rests is the symmetry of fundamental particles.