Exact solutions of N-dimensional harmonic oscillator via Laplace transformation

doi:10.1088/1009-1963/14/6/003

中国物理B ›› 2005, Vol. 14 ›› Issue (6): 1075-1076.doi: 10.1088/1009-1963/14/6/003

Exact solutions of N-dimensional harmonic oscillator via Laplace transformation

陈刚

Department of physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China; Materials Physics and Equipments Institute of Shaoxing University, Shaoxing 312000, China

收稿日期:2004-07-25 修回日期:2004-11-01 出版日期:2005-05-27 发布日期:2005-05-27

Exact solutions of N-dimensional harmonic oscillator via Laplace transformation

Chen Gang (陈刚)

Department of physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China; Materials Physics and Equipments Institute of Shaoxing University, Shaoxing 312000, China

Received:2004-07-25 Revised:2004-11-01 Online:2005-05-27 Published:2005-05-27

摘要/Abstract

摘要： The N-dimensional Schr?dinger equation for the harmonic oscillator is reduced to a first-order differential equation in terms of the Laplace transformation and the exact bound state solutions are derived. It is shown that this method to solve the Schr?dinger equation may serve as a substitute for the standard functional, analytical approach also in lower dimensions.

关键词: bound state, harmonic oscillator, Laplace transformation

Abstract: The N-dimensional Schr?dinger equation for the harmonic oscillator is reduced to a first-order differential equation in terms of the Laplace transformation and the exact bound state solutions are derived. It is shown that this method to solve the Schr?dinger equation may serve as a substitute for the standard functional, analytical approach also in lower dimensions.

Key words: bound state, harmonic oscillator, Laplace transformation

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

03.65.Db (Functional analytical methods) 02.30.Uu (Integral transforms)

陈刚. Exact solutions of N-dimensional harmonic oscillator via Laplace transformation[J]. 中国物理B, 2005, 14(6): 1075-1076.

Chen Gang (陈刚). Exact solutions of N-dimensional harmonic oscillator via Laplace transformation[J]. Chinese Physics, 2005, 14(6): 1075-1076.

[1]	Cong Wang(王聪) and Xiao-Qi Wang(王晓琦). Thermoelectric signature of Majorana zero modes in a T-typed double-quantum-dot structure[J]. 中国物理B, 2023, 32(3): 37304-037304.
[2]	Yi-Cai Zhang(张义财). Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system[J]. 中国物理B, 2022, 31(5): 50311-050311.
[3]	Hongzhen Tang(唐宏珍), Peng Hu(胡鹏), Da-Jian Cui(崔大健), Hong Xiang(向红), and Dezhuan Han(韩德专). Bound states in the continuum in metal—dielectric photonic crystal with a birefringent defect[J]. 中国物理B, 2022, 31(10): 104209-104209.
[4]	Shangtong Jia(贾尚曈), Zhi Li(李智), and Jianjun Chen(陈建军). Brightening single-photon emitters by combining an ultrathin metallic antenna and a silicon quasi-BIC antenna[J]. 中国物理B, 2022, 31(1): 14209-014209.
[5]	Jianfeng Huang(黄剑峰), Qianju Song(宋前举), Peng Hu(胡鹏), Hong Xiang(向红), and Dezhuan Han(韩德专). Bound states in the continuum on perfect conducting reflection gratings[J]. 中国物理B, 2021, 30(8): 84211-084211.
[6]	Yuxiang Gao(高于翔), Xin Jin(金鑫), Yixuan Gao(高艺璇), Yu-Yang Zhang(张余洋), and Shixuan Du(杜世萱). Electronic structures of vacancies in Co₃Sn₂S₂[J]. 中国物理B, 2021, 30(7): 77102-077102.
[7]	Wei-Jiang Gong(公卫江), Yu-Hang Xue(薛宇航), Xiao-Qi Wang(王晓琦), Lian-Lian Zhang(张莲莲), and Guang-Yu Yi(易光宇). Suppression of leakage effect of Majorana bound states in the T-shaped quantum-dot structure[J]. 中国物理B, 2021, 30(7): 77307-077307.
[8]	Fu-Bin Yang(羊富彬), Gan Ren(任淦), and Lin-Guo Xie(谢林果). Phase- and spin-dependent manipulation of leakage of Majorana mode into double quantum dot[J]. 中国物理B, 2021, 30(7): 78505-078505.
[9]	Lei Jiang(姜磊), Li Lai(赖莉), Tao Yu(蔚涛), Maokang Luo(罗懋康). Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency[J]. 中国物理B, 2021, 30(6): 60502-060502.
[10]	Bing-Sheng Lin(林冰生) and Tai-Hua Heng(衡太骅). Connes distance of 2D harmonic oscillators in quantum phase space[J]. 中国物理B, 2021, 30(11): 110203-110203.
[11]	Ning Wang(王宁), Xingtao An(安兴涛), and Shuhui Lv(吕树慧). Detection of spin current through a quantum dot with Majorana bound states[J]. 中国物理B, 2021, 30(10): 100302-100302.
[12]	韩张华, 姜辉, 谭智勇, 曹俊诚, 蔡阳健. Symmetry-broken silicon disk array as an efficient terahertz switch working with ultra-low optical pump power[J]. 中国物理B, 2020, 29(8): 84209-084209.
[13]	刘佳, 李科曼, 迟锋, 付振国, 侯跃飞, 王志刚, 张平. Probing the Majorana bound states in a hybrid nanowire double-quantum-dot system by scanning tunneling microscopy[J]. 中国物理B, 2020, 29(7): 77302-077302.
[14]	陈文祥, 王瑞强, 胡梁宾. Effects of interface bound states on the shot noise in normal metal-low-dimensional Rashba semiconductor tunnel junctions with induced s-wave pairing potential[J]. 中国物理B, 2019, 28(5): 57201-057201.
[15]	Azmat Iqbal, Kiran Humayun, Sana Maqsood, Saba Jawaid, Afaq Ahmad, Amin Ur Rahman, Bakht Amin Bacha. Quantum photodetachment of hydrogen negative ion in a harmonic potential subjected to static electric field[J]. 中国物理B, 2019, 28(2): 23201-023201.

Exact solutions of N-dimensional harmonic oscillator via Laplace transformation

Exact solutions of N-dimensional harmonic oscillator via Laplace transformation

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0