A reduced-order representation of the Schrodinger equation

作者：Cheng Ming C^*

来源：AIP Advances, 2016, 6(9): 095121.

DOI：10.1063/1.4963835

A reduced-order-based representation of the Schrodinger equation is investigated for electron wave functions in semiconductor nanostructures. In this representation, the Schrodinger equation is projected onto an eigenspace described by a small number of basis functions that are generated from the proper orthogonal decomposition (POD). The approach substantially reduces the numerical degrees of freedom (DOF's) needed to numerically solve the Schrodinger equation for the wave functions and eigenstate energies in a quantum structure and offers an accurate solution as detailed as the direct numerical simulation of the Schrodinger equation. To develop such an approach, numerical data accounting for parametric variations of the system are used to perform decomposition in order to generate the POD eigenvalues and eigenvectors for the system. This approach is applied to develop POD models for single and multiple quantum well structure. Errors resulting from the approach are examined in detail associated with the selected numerical DOF's of the POD model and quality of data used for generation of the POD eigenvalues and basis functions. This study investigates the fundamental concepts of the POD approach to the Schrodinger equation and paves a way toward developing an efficient modeling methodology for large-scale multi-block simulation of quantum nanostructures.

• 出版日期2016-9