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Abstract: Hooke’s Atom describes a system that acts as a crude approximation of a helium atom. Two electrons are repelled by the Coulomb interaction, and a harmonic oscillator replaces the nuclear force. Its potential contains two terms, an x^2 term and a 1/|x| term. This system is notable because it is one of the rare instances where genuine coulomb interactions yield an exactly solvable Schrodinger equation. Previous research reveals that these solutions exist only for an infinite set of certain discrete values of the frequency of the harmonic oscillator. This thesis explores a numerical method to determine the eigenvalues of Hooke’s Atom. The potential is placed inside of an infinite square well and regularized to avoid the singularity at the origin. Matrix mechanics are used to determine the energy eigenvalues. This thesis reveals a numerical solution with an arbitrary harmonic oscillator frequency, and reveals more solutions than the analytical method.

Advisor: Professor Rufus Boyack

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