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

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Exact solutions of N-dimensional harmonic oscillator via Laplace transformation

陈刚   

  1. 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)   

  1. 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

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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)