Wilson, Gwyn — Resonant Transmission in Smooth Barriers

Resonant transmission is a well-known effect in quantum mechanics, often studied in undergraduate physics courses. There is a resonant behaviour in the transmission probability for a square barrier potential. However, this effect is not seen in a gaussian barrier. The lack of resonances is investigated for barriers that start with a square shape and are deformed into a smoother one, with the transmission probability being calculated numerically. Doing so gives insight into the behaviour of the resonances and how the barrier shape can affect their presence.