The Schrödinger Equation Solution in 1-Dimension

In the paper Schrödinger Equation we describe where the equation comes from in the realm of Quantum Mechanics and how it is solved in the one dimensional case. The solution serves as a good example of solving a separable partial differential equation that satisfies the Sturm-Liouville conditions (reviewed in the Appendix). It also provides a real-world application of Fourier analysis. The paper is meant as an introductory study guide for someone who has heard about Quantum Mechanics and the importance of the Schrödinger equation but never had the chance to study it formally. The author always appreciates hearing about any errors or typos in the paper.