A Finite Element Method Solver for Time-Dependent and Stationary Schrodinger Equations with a Generic Potential  

作　　者：A.Soba 

机构地区：[1]Computer Applications in Science&Engineering,Barcelona Supercomputing Center,c/Jordi Girona,31,08034,Barcelona,Spain

出　　处：《Communications in Computational Physics》2009年第5期914-927,共14页计算物理通讯（英文）

摘　　要：A general finite element solution of the Schrodinger equation for a onedimensional problem is presented.The solver is applicable to both stationary and time-dependent cases with a general user-selected potential term.Furthermore,it is possible to include external magnetic or electric fields,as well as spin-orbital and spinmagnetic interactions.We use analytically soluble problems to validate the solver.The predicted numerical auto-states are compared with the analytical ones,and selected mean values are used to validate the auto-functions.In order to analyze the performance of the time-dependent Schrodinger equation,a traveling wave package benchmark was reproduced.In addition,a problem involving the scattering of a wave packet over a double potential barrier shows the performance of the solver in cases of transmission and reflection of packages.Other general problems,related to periodic potentials,are treated with the same general solver and a Lagrange multiplier method to introduce periodic boundary conditions.Some simple cases of known periodic potential solutions are reported.

关 键 词：One dimensional finite element methods time dependent Schrodinger equation periodic boundary conditions quantum computer simulation 

分 类 号：O17[理学—数学]