Improvements to Diminish Wave Reflection in Simulation of Quantum Tunneling

Imagine a particle that is fired at a barrier of some kind. In quantum mechanics, there is a concept known as "tunneling", which suggests that there is a possibility the particle may "tunnel" through to the other side, rather than classically get reflected. I have previously developed a Python code numerically simulating a Gaussian wave packet to represent a particle tunneling through a double potential barrier across varying momentum values. In search of quasi-bound states, an issue arose where the boundaries of the simulation act as an infinite energy wall, rather than demonstrating the natural evolution of the wave, interrupting the desired simulation as the wave is reflected back into the data collection. In this poster, I highlight several solutions I have attempted to address this issue. I initially tried simply changing the boundary conditions. In my next attempt, I then added a damping factor to the boundaries. Now, I am attempting to redefine the spatial grid that demonstrates the visual evolution. Changing this requires manipulating the matrix that the wave packet is originally solved in, ideally allotting more time for the simulation to be run, yielding more accurate results and revealing at what energies the particle remains quasi-bound, and for how long.