Physical Sciences and Mathematics Commons^™

Effect Of Compactified Dimensions On The Ground State Energy Of The Hydrogen Atom, Floyd Maseda

Honors Theses

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 …