# Implementation of Schroedinger's equation - mathematical concepts.

1. Sep 5, 2011

### DiracRules

Hi all!

I'm not sure whether this is the correct section to post my question.
I'm learning the program OpenFOAM, implemented in C++ and I'd like to implement schroedinger's equation $i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{x},t)=-\frac{\hbar^2}{2m}\nabla^2 \Psi(\mathbf{x},t) + V\Psi(\mathbf{x},t)$

The solvers are already implemented to solve REAL differential equations (like the diffusion one, $\frac{\partial T}{\partial t}=D\nabla T$).

So, the main question is: is there a way (e.g., using matrices...) to solve two PDE in a way such that the result gives me the real and the complex part of the solution?

In a http://www.google.com/url?sa=t&sour...ckTTmsCg&sig2=oEoBEr0nWQuH6AA-k8_d3Q&cad=rja" I found a script that made something like that (see paragraph 4), but I did not understand why he used 3x3 matrices (so that the output vector is $(Re\Psi, Im\Psi, 0)$) and not 2x2 matrices (to have directly $(Re\Psi, Im\Psi)$).
How can I describe the behaviour of the complex unit using matrices?

Sorry if it is not so clear...
If I am posting in the wrong place, please tell me where to post :D
Thank you all!!!

Last edited by a moderator: Apr 26, 2017