For my physics Master’s thesis, I studied the theoretical behavior of electrons confined between a charged metal plate and a two-dimensional gas. Physicists manipulate these electrons by introducing charged metal “gates” between the gas layer and plate. The idea is that the reliable control of electrons in this manner could lead to the development of an experimental quantum computer.
“Bound” electrons are confined to a potential well (defined by the metal gates). When one or both walls of this well are lowered (the gates are removed), the electron becomes “unbound.” I studied the states that exist in wells like the one shown, known as “quasibound” states. In this case, electrons are free to travel to the right in the purely unbound region of the potential landscape, but those that are travelling to the left can get stuck for a time in the step you see from x=0 to x=a. These quasibound wavefunctions can be characterized by discrete complex numbers known as eigenvalues, which are identified graphically in the colored images shown.