Applied Math Minor

Abstract

Involve NEwtons Method, swap out the paper

In this paper we derived a solution to Schrodinger's equation for the Hydrogen Atom, and confirm our derived formula with experimental data. 

To find our formula we relied on the De Broglie Theory of wave-particle duality and the Bohr model of the electron. Then we determined separable solutions via Fourier's method, which enables the identification of generic solutions. After this, we used the properties of the separated solutions to determine the allowable energy levels for the Hydrogen atom. 

This paper proceeded to verify the results experimentally by interpolating data obtained from the emission spectra of Helium and Mercury, which was found in the lab via a light spectrometer. We experimentally identifies Planck's constant, which was used to solve for the energy levels predicted by our theoretical exploration. Finally, it analyzes the error of the results and explores the implications. We conclude with an analysis of the significance of the results identified.

We were told to find an application of linear algebra, to research the application, and to write a paper discussing it. We researched and implemented covariance transformations used to help predict the movement of satellites.