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Physics and the natural world have been studied by humans since the first person wondered ‘Why?’ The Schrödinger equation is important because it attempts to describe a relatively new (to us) and unfamiliar part of our universe, behavior of subatomic particles, and helps modern scientists uncover secrets that have proven useful in technology and explaining our origins. The time dependent Schrödinger equation can be derived from various starting points in Classical such as the equation of a wave, the time independent Schrödinger equation, and Hamilton-Jacobi equations. Why Quantum mechanics exists, useful applications, and cases when it fails or is inaccurate are often not understood or even easy to explain to people uninvolved in physical studies. Not only do I hope for someone to be more educated on the topic after encountering this project, but I, myself, have learned a great deal more about the advanced topics I am interested in.
Class: Math 488 – Senior Capstone
Grand Forks, ND
Physics, Schrodinger Equation, Quantum Mechanics, Classical Mechanics, Differential Equations, Mathematics, Derivations
Swanson, Sydney, "Four Derivations of Schrödinger’s Time Dependent Equation" (2018). Essential Studies UNDergraduate Showcase. 13.