Authors :
Dr. Ismail Abbas
Volume/Issue :
Volume 8 - 2023, Issue 12 - December
Google Scholar :
http://tinyurl.com/54t3ye6y
Scribd :
http://tinyurl.com/ydxbmu62
DOI :
https://doi.org/10.5281/zenodo.10437573
Abstract :
In a previous paper we studied the extension
of transition matrix chains B from the heat diffusion
equation to the numerical statistical solution of the time-
independent Schrödinger equation in a spatial dimension
x.
In this paper, we propose the extension of transition
matrix chains B to the numerical statistical solution of
the time-independent Schrödinger equation in two
spatial dimensions x,y.
Extending physical transition matrix chains B to
the solution of the time-independent Schrödinger
equation requires respecting certain limitations of the
bases that we briefly explain in this article.
We present the numerical statistical solution via
matrix B in two illustrative situations, namely the two-
dimensional heat diffusion equation and the two-
dimensional infinite potential well where the numerical
results are surprisingly accurate.
In a previous paper we studied the extension
of transition matrix chains B from the heat diffusion
equation to the numerical statistical solution of the time-
independent Schrödinger equation in a spatial dimension
x.
In this paper, we propose the extension of transition
matrix chains B to the numerical statistical solution of
the time-independent Schrödinger equation in two
spatial dimensions x,y.
Extending physical transition matrix chains B to
the solution of the time-independent Schrödinger
equation requires respecting certain limitations of the
bases that we briefly explain in this article.
We present the numerical statistical solution via
matrix B in two illustrative situations, namely the two-
dimensional heat diffusion equation and the two-
dimensional infinite potential well where the numerical
results are surprisingly accurate.
