Date of Award

Spring 5-11-2012

Degree Type

Honors College Thesis


Physics and Astronomy

First Advisor

Khin Maung Maung

Advisor Department

Physics and Astronomy


The three-dimensional Hydrogen atom has been explored extensively, and a wavefunction and energy expression can be found in closed form. Little work, however, has been done with higher-dimensional atoms. This discussion focuses on the effects of adding first one then two compactified dimensions to a Hydrogen atom. The metric of the 4-D Hydrogen atom is taken to be R3 × S1 while the 5-D metric is taken to be R3 × S2. We first determine the form of the Laplacian operator in each space and use it to find the respective atomic potentials. The variational method is used to determine an upper bound on the ground state energy as a function of the size of the extra dimension(s). Equating the 4- and 5-D variational energy functions with the experimentally confirmed 3-D Hydrogen atom ground state, an upper bound on the size the compactied dimension(s) must be in order to have not yet been detected is calculated.