A discrete geometric approach to solving time independent Schroedinger equation

Journal Article · Sun Feb 20 00:00:00 EST 2011 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.11.007· OSTI ID:21499770

Specogna, Ruben ^[1]; Trevisan, Francesco ^[1]

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1. Universita di Udine, Via delle Scienze 208, I-33100 Udine (Italy)

The time independent Schroedinger 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 Schroedinger 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.

• OSTI ID: 21499770
• Journal Information: Journal of Computational Physics, Vol. 230, Issue 4; Other Information: DOI: 10.1016/j.jcp.2010.11.007; PII: S0021-9991(10)00609-1; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ANISOTROPY
COMPUTERIZED SIMULATION
EIGENVALUES
FINITE ELEMENT METHOD
GEOMETRY
INTEGRALS
NANOSTRUCTURES
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL SOLUTIONS
MATHEMATICS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
WAVE EQUATIONS