The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation of the spectrum of a Schrödinger operator with a disordered potential. Unlike plane waves or Bloch waves that arise as Schrödinger eigenfunctions for period...

X iv :q ua nt -p h/ 03 12 04 1v 1 4 D ec 2 00 3 Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton Jacobi Formalism ∗ S. Sree Ranjani , A.K. Kapoor ‡ and P.K. Panigrahi § a School of Physics, University of Hyderabad, Hyderabad 500 046, India b Physical Research Laboratory Navrangpura, Ahmedabad, 380009, India Abstract We obtain the band e...

— In this work, we use the regularized sampling method to compute the eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval. We work out an example by computing a few eigenvalues and their corresponding eigenfunctions.

We consider an eigenvalue problem for a divergence form elliptic operator Aε with locally perturbed high contrast periodic coefficients. Periodicity size ε is a small parameter. Local perturbation of coefficients for such operator could result in emergence of localized waves eigenfunctions with corresponding eigenvalues lying in the gaps of the Floquet-Bloch spectrum. We prove that, for a doubl...

The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for any aperture, the eigenvalues accumulate below the threshold of the essential spectrum: For a small distance from the essential spectrum, the number of eigenvalues farther fro...

e Eigenvalues on Polyhedra Martin COSTABEL & Monique DAUGE Abstract. In a convex polyhedron, a part of the Lam e eigenvalues with hard simple support boundary conditions does not depend on the Lam e coe cients and coincide with the Maxwell eigenvalues. The other eigenvalues depend linearly on a parameter s linked to the Lam e coe cients and the associated eigenmodes are the gradients of the Lap...