MULTISCALE METHOD FOR QUANTUM MECHANICS
The commonly used basis set calculation in quantum mechanics employs orbital functions as the basis functions in the approximation of wave functions for solving Schrodinger * equations. This approach typically yields a full matrix in the discrete equations due to the nonlocality of the orbital functions. In this work we first introduce an orbital HP Cloud (OHPC) method under the partition of unity framework with orbital functions as intrinsic bases and polynomials as extrinsic bases for solving Schrodinger equation. This approach yields compact supports in the approximation functions and results in a banded matrix in the discretization of Schrodinger equation. It is shown that when reproduction of orbital basis functions is introduced in OHPC approximation as an intrinsic enrichment, higher order extrinsic polynomial enrichment is only needed in the vicinity of the nuclei. We then extend the proposed computational quantum mechanics methods to multiscale modeling of quantum systems such as quantum dot arrays based on asymptotic expansion method. Proper coarse-fine scale coupling functions for electron energy and wave function are introduced and solved for obtaining the homogenized effective mass, confinement potential and Hamiltonian. An iterative method is then introduced to further enhance the solution accuracy of the proposed multiscale method for quantum systems.
partition of unity HP cloud quantum mechanics multiscale Schroedinger equation
Jiun-Shyan Chen Wei Hu
Civil & Environmental Engineering Department University of California at Los Angeles, USA
国际会议
广州
英文
1-11
2010-12-17（万方平台首次上网日期，不代表论文的发表时间）