  We study the spectral approximation of a second-order elliptic differential
eigenvalue problem that arises from structural vibration problems using
isogeometric analysis. In this paper, we generalize recent work in this
direction. We present optimally blended quadrature rules for the isogeometric
spectral approximation of a diffusion-reaction operator with both Dirichlet and
Neumann boundary conditions. The blended rules improve the accuracy and the
robustness of the isogeometric approximation. In particular, the optimal
blending rules minimize the dispersion error and lead to two extra orders of
super-convergence in the eigenvalue error. Various numerical examples
(including the Schr$\ddot{\text{o}}$dinger operator for quantum mechanics) in
one and three spatial dimensions demonstrate the performance of the blended
rules.
