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.