On numerical solutions of the time-dependent Schr\"odinger equation

• URL: http://arxiv.org/abs/2306.00997v1
• Date: Tue, 30 May 2023 15:22:09 GMT
• Title: On numerical solutions of the time-dependent Schr\"odinger equation
• Authors: Wytse van Dijk
• Abstract summary: An explicit approach to obtaining numerical solutions of the Schr"odinger equation is presented. Because of its explicit nature, the algorithm can be readily extended to systems with a higher number of spatial dimensions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We review an explicit approach to obtaining numerical solutions of the Schr\"odinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with several examples. Because of its explicit nature, the algorithm can be readily extended to systems with a higher number of spatial dimensions. We show that the method also generalizes the staggered-time approach of Visscher and allows for the accurate calculation of the real and imaginary parts of the wave function separately.

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