Solving the Schrodinger Equation for Infinite Potential Wells

Abstract

We solve the Schrodinger equation, after a brief introduction to quantum mechanics, for systems where we have zero potential energy within a given region, and infinite potential energy elsewhere. First, square wells are analyzed and generalized to the N-dimensional case. We then look at radial wells in two and three dimensions, discussing how the number of dimensions alters the solutions and the possibility of higher-dimensional generalization.