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Geometrical structure of Laplacian eigenfunctions
Laplace operator eigenfunctions eigenvalues localization
2012/6/25
We review the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level...
Estimates on Neumann eigenfunctions at the boundary, and the "Method of Particular Solutions" for computing them
Estimates Neumann eigenfunctions Spectral Theory Analysis of PDEs
2011/9/1
Abstract: We consider the "Method of particular solutions" for numerically computing eigenvalues and eigenfunctions of the Laplacian $\Delta$ on a smooth, bounded domain Omega in RR^n with either Diri...
The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr-Sommerfeld quantization condition, revisited
he semiclassical limit of eigenfunctions Schrö dinger equation Bohr-Sommerfeld quantization condition
2010/12/1
Consider the semiclassical limit, as the Planck constant ~ ! 0, of bound states of a quantum particle in a one-dimensional potential well. We justify the semiclassical asymptotics of eigenfunctions an...