Authors :
Dr. Ismail Abbas
Volume/Issue :
Volume 8 - 2023, Issue 12 - December
Google Scholar :
http://tinyurl.com/2a268dkp
Scribd :
http://tinyurl.com/bdd948nj
DOI :
https://doi.org/10.5281/zenodo.10521199
Abstract :
In previous papers we have studied the
extension of transition matrix chains B to the numerical
statistical solution of the time-independent Schrödinger
equation in one two dimensions x,y.
In this paper we examine the extension of B-
transition matrix chains to the numerical statistical
solution of the time-independent Schrödinger equation in
the three dimensions x, y, z.
However, extending the physical transition matrix
chains B to the solution of the time-independent
Schrödinger equation requires respecting certain
limitations of the bases which we briefly explain in this
article.
We present the numerical statistical solution via B-
matrix chains in two illustrative examples, namely the
three-dimensional time-dependent heat diffusion
equation and the quantum particle in a three-
dimensional infinite potential well. The numerical results
are surprisingly accurate.
In previous papers we have studied the
extension of transition matrix chains B to the numerical
statistical solution of the time-independent Schrödinger
equation in one two dimensions x,y.
In this paper we examine the extension of B-
transition matrix chains to the numerical statistical
solution of the time-independent Schrödinger equation in
the three dimensions x, y, z.
However, extending the physical transition matrix
chains B to the solution of the time-independent
Schrödinger equation requires respecting certain
limitations of the bases which we briefly explain in this
article.
We present the numerical statistical solution via B-
matrix chains in two illustrative examples, namely the
three-dimensional time-dependent heat diffusion
equation and the quantum particle in a three-
dimensional infinite potential well. The numerical results
are surprisingly accurate.
