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A discrete geometric approach to solving time independent Schrödinger equation
- Source :
-
Journal of Computational Physics . Feb2011, Vol. 230 Issue 4, p1370-1381. 12p. - Publication Year :
- 2011
-
Abstract
- Abstract: The time independent Schrödinger 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 Schrödinger 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 230
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 57072844
- Full Text :
- https://doi.org/10.1016/j.jcp.2010.11.007