Efficient simulation of the Schroedinger equation with a piecewise constant positive potential

Yang Xuxin; Rasila Antti; Sottinen Tommi

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Efficient simulation of the Schroedinger equation with a piecewise constant positive potential

机译：分段恒定正电位的Schrodinger方程的高效仿真

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摘要

We introduce a new method for the Monte Carlo simulation of a weak solution of the Schrodinger-type equation where the potential is piecewise constant and positive. The method, called the killing walk-on-spheres algorithm, combines the classical walk-on-spheres algorithm with killing that can be determined by using panharmonic measures. This paper continues our earlier work in which simulation of the solutions of the Yukawa and the Helmholtz partial differential equations were developed. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

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《Mathematics and computers in simulation》 |2019年第12期|315-323|共9页
作者
Yang Xuxin; Rasila Antti; Sottinen Tommi;
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作者单位

Hunan First Normal Univ Dept Math Changsha 410205 Hunan Peoples R China;

Guangdong Technion Israel Inst Technol Coll Sci 241 Daxue Rd Shantou 515063 Guangdong Peoples R China;

Univ Vaasa Sch Technol & Innovat POB 700 FIN-65101 Vaasa Finland;

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正文语种 eng
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关键词
Brownian motion; Killing walk-on-spheres; Harmonic measure; Numerical algorithm; Yukawa equation; Schrodinger equation;

机译：布朗运动杀死步行领域;谐波测量;数值算法;汤川方程;薛定inger方程;

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1. Efficient simulation of the Schroedinger equation with a piecewise constant positive potential [J] . Yang Xuxin, Rasila Antti, Sottinen Tommi Mathematics and computers in simulation . 2019,第DECa期

机译：分段恒定正电位的Schrodinger方程的高效仿真
2. Solutions of the Schroedinger equation for piecewise harmonic potentials: Remarks on the asymptotic behavior of the wave functions [J] . Mazzitelli Francisco D., Mazzitelli Martin D., Soubelet Pedro I. American journal of physics . 2017,第10期

机译：分段谐波电位施罗德格方程的解决方案：关于波函数的渐近行为的备注
3. EXISTENCE OF POSITIVE SOLUTIONS OF SCHROEDINGER EQUATIONS WITH VANISHING POTENTIALS [J] . Eduard Toon, Pedro Ubilla Discrete and continuous dynamical systems . 2020,第10期

机译：消失潜力施罗德格方程正解的存在
4. Efficient Solution of the Schroedinger-Poisson Equations in Semiconductor Device Simulations [C] . Alex Trellakis, Till Andlauer, Peter Vogl International Conference on Large-Scale Scientific Computing . 2006

机译：半导体器件模拟中Schroedinger-Poisson方程的有效解
5. On the existence of infinite bump solutions of nonlinear Schroedinger equations with periodic potentials [D] . Thandi, Neeza. 1995

机译：具有周期性潜力的非线性施格格方程无限凸块解的存在
6. BDflex: A method for efficient treatment of molecular flexibility in calculating protein-ligand binding rate constants from Brownian dynamics simulations [O] . Nicholas Greives, Huan-Xiang Zhou -1

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7. Solutions of the Schroedinger equation for piecewise harmonic potentials: remarks on the asymptotic behavior of the wave functions [O] . Mazzitelli, F. D., Mazzitelli, M. D., Soubelet, P. I. 2017

机译：分段调和的schroedinger方程的解潜力：关于波函数的渐近行为的评论
8. Piecewise Analytical Perturbation Series Methods for Solving Linear Ordinary Differential Equations. 2. The Radial Schroedinger Equations [R] . Adam, G. 1984

机译：求解线性常微分方程的分段解析扰动级数法。 2.径向schroedinger方程

Efficient simulation of the Schroedinger equation with a piecewise constant positive potential

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