STATIONARY SOLUTIONS OF THE NONLINEAR SCHR?DINGER EQUATION FOR NEUTRAL ATOMS IN A HARMONIC TRAP

YAN KE-ZHU; TAN WEI-HAN

doi:10.7498/aps.48.1185

Citation:

STATIONARY SOLUTIONS OF THE NONLINEAR SCHR?DINGER EQUATION FOR NEUTRAL ATOMS IN A HARMONIC TRAP

YAN KE-ZHU, TAN WEI-HAN

Acta Phys. Sin., 1999, 48(7): 1185-1191.

doi: 10.7498/aps.48.1185

Abstract
We present a general method to solve the stationary nonlinear Schr?dinger equation (NLSE) with an external potential. We apply it to the stationary states of NLSE for neutral atoms in a harmonic trap. We discuss the problems of convergence and normalization of NLSE wave function. The accuracy of calculation is analyzed.
Authors and contacts
YAN KE-ZHU,

TAN WEI-HAN

1.
上海大学物理系,上海 201800
References

Cited By

[1]	WANG Gangwei, TAN Zixuan. Similarity transformations and exact solutions of the generalized (n + 1)-dimensional Schrödinger equation with (2m + 1)-th order nonlinear terms and spatiotemporally varying coeffcients. Acta Physica Sinica, 2025, 74(10): . doi: 10.7498/aps.74.20250225
[2]	Gong Rui-Zhi, Wang Deng-Shan. Whitham modulation theory of defocusing nonlinear Schrödinger equation and the classification and evolutions of solutions with initial discontinuity. Acta Physica Sinica, 2023, 72(10): 100503. doi: 10.7498/aps.72.20230172
[3]	Rao Ji-Guang, Chen Sheng-An, Wu Zhao-Jun, He Jin-Song. General higher-order rogue waves in the space-shifted $\mathcal{PT}$-symmetric nonlocal nonlinear Schrödinger equation. Acta Physica Sinica, 2023, 72(10): 104204. doi: 10.7498/aps.72.20222298
[4]	Wen Jia-Mei, Bo Wen-Bo, Wen Xue-Kun, Dai Chao-Qing. Multipole vector solitons in coupled nonlinear Schrödinger equation with saturable nonlinearity. Acta Physica Sinica, 2023, 72(10): 100502. doi: 10.7498/aps.72.20222284
[5]	Li Min, Wang Bo-Ting, Xu Tao, Shui Juan-Juan. Study on the generation mechanism of bright and dark solitary waves and rogue wave for a fourth-order dispersive nonlinear Schrödinger equation. Acta Physica Sinica, 2020, 69(1): 010502. doi: 10.7498/aps.69.20191384
[6]	Jiang Tao, Huang Jin-Jing, Lu Lin-Guang, Ren Jin-Lian. Numerical study of nonlinear Schrödinger equation with high-order split-step corrected smoothed particle hydrodynamics method. Acta Physica Sinica, 2019, 68(9): 090203. doi: 10.7498/aps.68.20190169
[7]	Cui Shao-Yan, Lü Xin-Xin, Xin Jie. Collapse and evolution of wave field based on a generalized nonlinear Schrdinger equation. Acta Physica Sinica, 2016, 65(4): 040201. doi: 10.7498/aps.65.040201
[8]	Li Pan, Shi Lei, Mao Qing-He. A fourth-order Runge-Kutta in the interaction picture algorithm for simulating coupled generalized nonlinear Schrödinger equation and its error analysis. Acta Physica Sinica, 2013, 62(15): 154205. doi: 10.7498/aps.62.154205
[9]	Song Sha-Sha, Meng Jun-Min, Song Shi-Yan, Wang Jing, Wang Jian-Bu. Numerical simulation of internal waves propagation in deep sea by nonlinear Schr?dinger equation. Acta Physica Sinica, 2010, 59(9): 6339-6344. doi: 10.7498/aps.59.6339
[10]	Song Shi-Yan, Wang Jing, Meng Jun-Min, Wang Jian-Bu, Hu Pei-Xin. Nonlinear Schr?dinger equation for internal waves in deep sea. Acta Physica Sinica, 2010, 59(2): 1123-1129. doi: 10.7498/aps.59.1123
[11]	Zhao Lei, Sui Zhan, Zhu Qi-Hua, Zhang Ying, Zuo Yan-Lei. Improvement and precision analysis of the split-step Fourier method in solving the general nonlinear Schr?dinger equation. Acta Physica Sinica, 2009, 58(7): 4731-4737. doi: 10.7498/aps.58.4731
[12]	Cheng Xue-Ping, Lin Ji, Wang Zhi-Ping. Asymptotic solutions of perturbed N-component nonlinear Schr?dinger equations. Acta Physica Sinica, 2007, 56(6): 3031-3038. doi: 10.7498/aps.56.3031
[13]	Gong Lun-Xun. Some new exact solutions of the Jacobi elliptic functions of NLS equation. Acta Physica Sinica, 2006, 55(9): 4414-4419. doi: 10.7498/aps.55.4414
[14]	Ruan Hang-Yu, Li Hui-Jun. Solution of the nonlinear Schr?dinger equation using the generalized Lie group reduction method. Acta Physica Sinica, 2005, 54(3): 996-1001. doi: 10.7498/aps.54.996
[15]	Zhang Jie-Fang, Xu Chang-Zhi, He Bao-Gang. The variable separation approach and study on solving the variable-coefficient nonlinear Schr?dinger equation. Acta Physica Sinica, 2004, 53(11): 3652-3656. doi: 10.7498/aps.53.3652
[16]	LIU JIAN-BO, CAI XI-PING. A MACROSCOPICAL SIMULATION SOLUTION TO THE ONE-DIMENSIONAL STATIONARY STATE SCHRDINGER EQUATION. Acta Physica Sinica, 2001, 50(5): 820-824. doi: 10.7498/aps.50.820
[17]	RUAN HANG-YU, CHEN YI-XIN. RING SOLITONS, DROMIONS, BREATHERS AND INSTANTONS OF THE NLS EQUATION. Acta Physica Sinica, 2001, 50(4): 586-592. doi: 10.7498/aps.50.586
[18]	TIAN QIANG, MA BEN-KUN. THE FORMATION AND PROPAGATION OF DOMAINS IN SUPERLATTICES DISCUSSED WITH NONLINEAR SCHR¨ODINGER EQUATION. Acta Physica Sinica, 1999, 48(11): 2125-2130. doi: 10.7498/aps.48.2125
[19]	QU ZHI-LIN, HU GANG. TIME-DEPENDENT SOLUTION OF THE FOKKER-PLANCK EQUATION OF NONLINEAR NONPOTENTIAL SYSTEMS. Acta Physica Sinica, 1992, 41(9): 1396-1405. doi: 10.7498/aps.41.1396
[20]	HU GANG. TIME DEPENDENT SOLUTION OF FOKKER-PLANCK EQUATION WITH NON-LINEAR DRIFT FORCE. Acta Physica Sinica, 1985, 34(5): 573-580. doi: 10.7498/aps.34.573

Catalog

Vol. 48, Issue 7 - 1999-04-05

Metrics

Abstract views: 8774
PDF Downloads: 702
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

STATIONARY SOLUTIONS OF THE NONLINEAR SCHR?DINGER EQUATION FOR NEUTRAL ATOMS IN A HARMONIC TRAP

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

STATIONARY SOLUTIONS OF THE NONLINEAR SCHR?DINGER EQUATION FOR NEUTRAL ATOMS IN A HARMONIC TRAP

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About