Please wait a minute...
Chinese Physics, 2006, Vol. 15(9): 1909-1913    DOI: 10.1088/1009-1963/15/9/001
RAPID COMMUNICATION   Next  

Iterative solutions for low lying excited states of a class of Schrödinger equation

R. Friedberga), T. D. Lee(李政道)a)b), and Zhao Wei-Qin(赵维勤)b)c)
a Physics Department, Columbia University, New York, NY 10027, USA ; b China Center of Advanced Science and Technology (CCAST/World Laboratory), Beijing 100080, China; c Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, China
Abstract  The convergent iterative procedure for solving the groundstate Schr?dinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.
Keywords:  iterative solution      low-lying excited state      convergence  
Received:  12 July 2006      Revised:  14 July 2006      Accepted manuscript online: 
PACS:  92.70.Mn (Impacts of global change; global warming)  
  92.60.hv (Pressure, density, and temperature)  
  93.30.Db (Asia)  
Fund: This research was supported in part by the U.S. Department of Energy (Grant No DE-FG02-92ER-40699) and the National\linebreak \makebox[1.6mm]{}Natural Science Foundation of China (Grant No 10547001).

Cite this article: 

R. Friedberg, T. D. Lee(李政道), and Zhao Wei-Qin(赵维勤) Iterative solutions for low lying excited states of a class of Schrödinger equation 2006 Chinese Physics 15 1909

[1] Meshfree-based physics-informed neural networks for the unsteady Oseen equations
Keyi Peng(彭珂依), Jing Yue(岳靖), Wen Zhang(张文), and Jian Li(李剑). Chin. Phys. B, 2023, 32(4): 040208.
[2] A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation
Yu Tan(谭渝) and Xiao-Lin Li(李小林). Chin. Phys. B, 2021, 30(1): 010201.
[3] Truncated series solutions to the (2+1)-dimensional perturbed Boussinesq equation by using the approximate symmetry method
Xiao-Yu Jiao(焦小玉). Chin. Phys. B, 2018, 27(10): 100202.
[4] A novel stable value iteration-based approximate dynamic programming algorithm for discrete-time nonlinear systems
Yan-Hua Qu(曲延华), An-Na Wang(王安娜), Sheng Lin(林盛). Chin. Phys. B, 2018, 27(1): 010203.
[5] Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method
Hu Dou(窦虎), Hongmei Ma(马红梅), Yu-Bao Sun(孙玉宝). Chin. Phys. B, 2016, 25(9): 094221.
[6] Dynamic properties of chasers in a moving queue based on a delayed chasing model
Ning Guo(郭宁), Jian-Xun Ding(丁建勋), Xiang Ling(凌翔), Qin Shi(石琴), Reinhart Kühne. Chin. Phys. B, 2016, 25(5): 050505.
[7] A local energy-preserving scheme for Klein–Gordon–Schrödinger equations
Cai Jia-Xiang (蔡加祥), Wang Jia-Lin (汪佳玲), Wang Yu-Shun (王雨顺). Chin. Phys. B, 2015, 24(5): 050205.
[8] Analysis for flow of Jeffrey fluid with nanoparticles
T. Hayat, Sadia Asad, A. Alsaedi. Chin. Phys. B, 2015, 24(4): 044702.
[9] A meshless algorithm with moving least square approximations for elliptic Signorini problems
Wang Yan-Chong (王延冲), Li Xiao-Lin (李小林). Chin. Phys. B, 2014, 23(9): 090202.
[10] Precipitation efficiency and its relationship to physical factors
Zhou Yu-Shu (周玉淑), Li Xiao-Fan (李小凡), Gao Shou-Ting (高守亭). Chin. Phys. B, 2014, 23(6): 064210.
[11] Effects of water and ice clouds on cloud microphysical budget:An equilibrium modeling study
Gao Shou-Ting (高守亭), Li Xiao-Fan (李小凡), Zhou Yu-Shu (周玉淑). Chin. Phys. B, 2014, 23(2): 024204.
[12] A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equation
Lv Zhong-Quan (吕忠全), Zhang Lu-Ming (张鲁明), Wang Yu-Shun (王雨顺). Chin. Phys. B, 2014, 23(12): 120203.
[13] Consensus problems of first-order dynamic multi-agent systems with multiple time delays
Ji Liang-Hao (纪良浩), Liao Xiao-Feng (廖晓峰). Chin. Phys. B, 2013, 22(4): 040203.
[14] Variational-integral perturbation corrections of some lower excited states for hydrogen atoms in magnetic fields
Yuan Lin (袁琳), Zhao Yun-Hui (赵云辉), Xu Jun (徐军), Zhou Ben-Hu (周本胡), Hai Wen-Hua (海文华). Chin. Phys. B, 2012, 21(10): 103103.
[15] A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation
Zhang Rong-Pei(张荣培),Yu Xi-Jun(蔚喜军),and Zhao Guo-Zhong(赵国忠). Chin. Phys. B, 2011, 20(3): 030204.
No Suggested Reading articles found!