Emily Ragauss ’22; Cole Thumann ’22

**Majors: **Comprehensive Physics

**Faculty Collaborator:** Jonathan Brown, Physics

In Quantum Mechanics, often the goal of solving some problem is to determine the probability that a particle is in some specified location at some given time. Our groupâ€™squantum problem of interest is the resonant tunneling phenomena. In this setup, it ismost useful to find the probability that a particle tunnels through the barriers- thetransmission amplitude. There are very few tunneling problems one may solveanalytically in Quantum Mechanics. In our research, we began by solving many of themore simple problems analytically to build a basis of understanding for how we wouldsolve the complex resonance cases. Our method was a traditional Quantum Mechanicalapproach of assigning wave functions to specific regions of potential energy using theSchrodinger Equation. Next, using systems of equations, complex analysis, theequation for transmission amplitude, and dimensional analysis, we expressed oursolution for the transmission amplitude. We later approached more variable setups ofresonant tunneling using the popular WKB approximation. Our results supported ourhypothesis of spikes in transmission probability for specific sweet-spot energy levels.