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