Symplectic Schemes and the Shooting Method for Eigenvalues of the Schrödinger Equation
LIU Xue-Shen, CHI Yu-Hua, DING Pei-Zhu
Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012
Symplectic Schemes and the Shooting Method for Eigenvalues of the Schrödinger Equation
LIU Xue-Shen;CHI Yu-Hua;DING Pei-Zhu
Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012
关键词 ：
02.70.-c ,
03.65.Ta
Abstract ： The one-dimensional time-independent Schrödinger equation is transformed into a Hamiltonian canonical equation by means of the Legendre transformation, then the symplectic schemes and a new shooting method extended to the eigenvalues of the Schrödinger equation. The method is applied to the calculations of one-dimensional harmonic oscillator, an anharmonic oscillator and the hydrogen atom. The numerical results are in good agreement with the exact ones.
Key words ：
02.70.-c
03.65.Ta
出版日期: 2004-09-01
:
02.70.-c
(Computational techniques; simulations)
03.65.Ta
(Foundations of quantum mechanics; measurement theory)
引用本文:
LIU Xue-Shen;CHI Yu-Hua;DING Pei-Zhu. Symplectic Schemes and the Shooting Method for Eigenvalues of the Schrödinger Equation[J]. 中国物理快报, 2004, 21(9): 1681-1684.
链接本文:
https://cpl.iphy.ac.cn/CN/
或
https://cpl.iphy.ac.cn/CN/Y2004/V21/I9/1681
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2004, Vol. 21 
