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Implementation of Schroedinger's equation - mathematical concepts.

  1. Sep 5, 2011 #1
    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 [itex]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)[/itex]

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

    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 [itex](Re\Psi, Im\Psi, 0)[/itex]) and not 2x2 matrices (to have directly [itex](Re\Psi, Im\Psi)[/itex]).
    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
  2. jcsd
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