Portable Scheme for Solving 1-D Time-Dependent Schrödinger Equation for Photo-Induced Dynamics of an Electron in Quantum Wells

We provide a simple numerical scheme for solving the ground state of an electron with arbitrary potential profile of quantum wells (QWs) as well as time-evolution under optical excitation by solving the (time-dependent) Schrödinger equation. Photo-induced migration of electron under asymmetric potential profile of QWs is demonstrated, which is highly sensitive to the wavelength of the applied light. Furthermore, electron behavior in multiple QWs is examined with and without irregularity in the period of multiple QWs. We believe that the current numerical scheme will be a useful tool for designing QWs to enhance photo-excitation and subsequent carrier migration without massive computational effort. We note that the current computational scheme is easy to code and perform, even on a laptop computer.