Math

As part of UIC's MURL program, I am leading a team of undergraduate students to investigate the emergence of quantum tunneling effects in linear Schrödinger equations. This phenomenon can be described with an analogy:

Imagine rolling a ball towards a hill and determining whether it reaches the peak based on how fast it’s rolled and how high the hill is. Then, assume we replace the ball with an electron and the hill with an electric potential. Classically, we expect that the electron will behave like the ball. That is, the electron will only crest the potential hill if it has sufficient energy. However, quantum physics indicates that, with low but non-zero probability, electrons can “tunnel” through potential barriers that they otherwise do not have the energy to cross.

This project is ongoing, and this page will be updated as we obtain results.