National Collegiate Honors Council


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UReCA: The NCHC Journal of Undergraduate Research and Creative Activity:


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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. [3] 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. [7]