Non-Relativistic Scenario of a Free Particle in an Infinite Cylindrical Potential Well

Abstract: There are various types of infinite potential well problems occurring in elementary quantum mechanics formalism. The infinite square well (one dimensional), cubical box and, spherical well are quite common in textbooks. In this paper, we consider a rather uncommon potential well, an infinite cylindrical well, and try to find its energy eigenvalues and eigenfunctions using Schr\"{o}dinger equation. We also plot some radial wavefunctions and density plots.