Abstract by Scott Johnstun
Physics and Astronomy
Jean-Francois Van Huele
Exact solutions to the time-dependent Schrodinger Equation for arbitrary quadratic potentials and moving wells
In courses on quantum mechanics, simple square well and harmonic oscillator potentials are studied frequently. We consider alternative methods that allow exact solutions to more general problems to be found, including arbitrary quadratic potentials and square wells with moving boundaries. Each method involves specific coordinate transformations. A method of solution akin to reducing the diffusion-convection equation to the heat equation is also applied to the Schrodinger equation.