Numerical methods for eigenvalue problems for boundary value problems involving PDEs, numerical examples, quantum waveguide problems, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, separation of variables, Estimates of eigenvalues in context of PDEs, finite volume method, Antennas, waveguides in optics and electromagnetic theory, comparison of methods, Dirichlet boundary conditions, 510, resonance, Laplace operator, eigenvalue problem, Other special methods applied to PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, Helmholtz equation, Fourier decomposition method, perturbation theory