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

TL;DR

This paper investigates the quantum behavior of a free particle in an infinite cylindrical potential well, deriving energy eigenvalues and eigenfunctions, and visualizing wavefunctions and densities to expand understanding of less common quantum systems.

Contribution

It provides a detailed analysis of the infinite cylindrical well, including solutions to the Schrödinger equation and graphical representations, which are less explored in standard quantum mechanics.

Findings

Derived energy eigenvalues for the cylindrical well

Obtained eigenfunctions and plotted radial wavefunctions

Visualized probability densities for the system

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.