We present a finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three dimensional cylindrically symmetric bounded domain with mixed  ...  Ultimately, we numerically treat them by means of a finite volume method. We consider a uniform, boundary conforming Delaunay mesh, which additionally conforms to the material interfaces.  ...  Conclusions We have presented a finite volume discretization of a cylindrically symmetric Wigner-Eisenbud problem, for computing a representative part of the spectral decomposition Figure 18 : The optimal  ...