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.
