Classical mechanics predicts that particles which do not have sufficient energy to overcome a potential barrier will not be able to pass to the other side of the barrier and will instead be reflected, with zero probability of transmission. Quantum tunneling describes the phenomenon in which particles with lower energy can still penetrate through a barrier, which would otherwise be classically forbidden. This worksheet will introduce the theory and applications of quantum tunneling. We will calculate the probability of quantum tunneling as a function of particle energy, particle mass, and barrier energy. Among the many applications of quantum tunneling, we will focus on the scanning tunneling microscope method used for atomic-level characterization of nanosurfaces, as well as resonant tunneling diodes used in nanoelectronics. Application uses the Maple Quantum Chemistry Toolbox.