Adaptive Multiscale Meshfree Method for Solving the Schrodinger Equation in Quantum Mechanics
The second part of this work extends the proposed computational quantum mechanics methods to multiscale modeling of quantum-dot semiconductors and quantum-dot arrays based on asymptotic expansion. Proper coarse-fine scale coupling functions for electron energy and wave function are introduced and solved for obtaining the fine scale information of effective mass and confinement potential. Consequently, the homogenized effective mass and confinement potential are obtained using the scale coupling functions. An iterative multiscale method by introducing Rayleigh quotient that uses the solution of the first order asymptotic expansion as the initial guess is also introduced.Franke and Schaback [47] provided some theoretical foundation of RBF method for solving PDEs. Wendland [115] derived error estimates of combining RBF and Galerkin method to solve PDE, and this combined approach leads to the sameanbsp;...
| Title | : | Adaptive Multiscale Meshfree Method for Solving the Schrodinger Equation in Quantum Mechanics |
| Author | : | Wei Hu |
| Publisher | : | ProQuest - 2008 |
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