A Statistical Numerical Solution for the Time-Independent Schrödinger Equation


Authors : Ismail Abbas

Volume/Issue : Volume 8 - 2023, Issue 12 - December

Google Scholar : http://tinyurl.com/mr2n54mc

Scribd : http://tinyurl.com/3wpky4tj

DOI : https://doi.org/10.5281/zenodo.10427237

Abstract : B-transition matrix chains resulting from the Cairo technique numerical statistical solution method have been successfully applied to statistically solve time- dependent partial differential equations in classical physics. This paper studies the extension of transition matrix chains B to the numerical statistical solution of the time-independent Schrödinger equation. However, extending the physical transition matrix chains B to the solution of the time-independent Schrödinger equation is not complicated but it is a bit long and requires respecting certain limitations of the bases which we briefly explain in this article. We present the numerical solution of matrix B in three illustrative examples, namely the heat diffusion equation, the quadratic potential well and the one- dimensional infinite potential well wherethe numerical results are surprisingly accurate.

B-transition matrix chains resulting from the Cairo technique numerical statistical solution method have been successfully applied to statistically solve time- dependent partial differential equations in classical physics. This paper studies the extension of transition matrix chains B to the numerical statistical solution of the time-independent Schrödinger equation. However, extending the physical transition matrix chains B to the solution of the time-independent Schrödinger equation is not complicated but it is a bit long and requires respecting certain limitations of the bases which we briefly explain in this article. We present the numerical solution of matrix B in three illustrative examples, namely the heat diffusion equation, the quadratic potential well and the one- dimensional infinite potential well wherethe numerical results are surprisingly accurate.

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