Dimension Reduction of the Schrödinger Equation with Coulomb and Anisotropic Confining Potentials
Dimension Reduction of the Schrödinger Equation with Coulomb and Anisotropic Confining Potentials
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DOI：
10.1137/13091436x
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发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
W. Bao;H. Jian;N. Mauser;Yong Zhang
中科院分区：
文献类型：
--
作者：
W. Bao;H. Jian;N. Mauser;Yong Zhang
我们考虑在一维或二维空间无限强约束极限下对具有库仑相互作用和各向异性约束势的三维（3D）薛定谔方程进行降维，并正式获得二维（2D）的表面绝热模型（SAM）或表面密度模型（SDM）以及一维的线绝热模型（LAM） (1D)。基于高效、准确的数值方案，提出了计算 SAM、SDM 和 LAM 模型基态和动力学的高效、准确的数值方法，以评估低维模型的有效潜力。它们被用来寻找基态和动力学方面从 3D 到 2D 以及 3D 到 1D 降维的数值收敛和收敛速率，这证实了文献中一些现有的降维分析结果。特别是，我们解释并证明了标准薛定谔-泊松系统在 2...
We consider dimension reduction for the three-dimensional (3D) Schrodinger equation with the Coulomb interaction and an anisotropic confining potential to lower-dimensional models in the limit of infinitely strong confinement in one or two space dimensions and obtain formally the surface adiabatic model (SAM) or surface density model (SDM) in two dimensions (2D) and the line adiabatic model (LAM) in one dimension (1D). Efficient and accurate numerical methods for computing ground states and dynamics of the SAM, SDM, and LAM models are presented based on efficient and accurate numerical schemes for evaluating the effective potential in lower-dimensional models. They are applied to find numerically convergence and convergence rates for the dimension reduction from 3D to 2D and 3D to 1D in terms of ground state and dynamics, which confirm some existing analytical results for the dimension reduction in the literature. In particular, we explain and demonstrate that the standard Schrodinger--Poisson system in 2...