Date of this Version
UReCA: The NCHC Journal of Undergraduate Research and Creative Activity: http://www.nchc-ureca.com/
The time-dependent Schrödinger equation (TDSE) is a fundamental law in understanding the states of many microscopic systems. Such systems occur in nearly all branches of physics and engineering, including high-energy physics, solid-state physics, and semiconductor engineering, just to name a few. A robust and efficient algorithm to solve this equation would be highly sought-after in these respective fields. This study utilizes the well-known method for solving the TDSE, the finite difference method (FDM), but with an important modification to conserve flux and analyze the 1-D case given well-known potentials. Numerical results that agree with theoretical predictions are reported.  It becomes evident, however, that solving the TDSE still involves challenging problems of scaling to higher dimensions and refined grids. This study shows that it is a promising, intuitive, and accurate method for linear domains over lower dimensions with arbitrary potentials.