High-order finite difference method for the Schrodinger equation on deforming domains

[摘要] A high-order finite difference discretisation of the Schrodinger equation on domains that deform in time is presented. For the domain deformation, a time-dependent coordinate transformation is used. The utilisation of summation-by-parts finite difference operators, combined with boundary conditions imposed weakly by a penalty technique, leads to a provably stable scheme. The convergence properties of the scheme are verified by numerical computations. The capabilities of the numerical scheme are demonstrated by simulations of Berry phases in deforming quantum billiards. (C) 2021 The Author(s). Published by Elsevier Inc.

[发布日期] 2021-10-15

[关键词] Finite difference methods;Quantum mechanics;High-order accuracy;Stabiity;Boundary treatment;deforming domain