The numerical modeling of nanoscale electron devices needs the development of accurate and efficient numerical methods, in
particular, for the numerical solution of the Schrödinger problem. If FEMs allow an accurate geometric representation of the device,
they lead to a discrete counterpart of Schrödinger problem in terms of a computationally heavy generalized eigenvalue problem.
Exploiting the geometric structure behind the Schrödinger problem, we will construct a numerically efficient discrete counterpart
of it, yielding to a standard eigenvalue problem. We will also show how the two approaches are only partially akin to each other
even when lumping is applied.
