Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Numerical simulation of three dimensional pyramid quantum dot
Journal of Computational Physics
Efficient solution of the Schroedinger-Poisson equations in layered semiconductor devices
Journal of Computational Physics
Discrete geometric approach for modelling quantization effects in nanoscale electron devices
Journal of Computational Electronics
| Hi-index | 31.45 |
The time independent Schrodinger equation stems from quantum theory axioms as a partial differential equation. This work aims at providing a novel discrete geometric formulation of this equation in terms of integral variables associated with precise geometric elements of a pair of three-dimensional interlocked grids, one of them based on tetrahedra. We will deduce, in a purely geometric way, a computationally efficient discrete counterpart of the time independent Schrodinger equation in terms of a standard symmetric eigenvalue problem. Moreover boundary and interface conditions together with non homogeneity and anisotropy of the media involved are accounted for in a straightforward manner. This approach yields to a sensible computational advantage with respect to the finite element method, where a generalized eigenvalue problem has to be solved instead. Such a modeling tool can be used for analyzing a number of quantum phenomena in modern nano-structured devices, where the accounting of the real 3D geometry is a crucial issue.