Symplectic Schemes and the Shooting Method for Eigenvalues of the Schrödinger Equation

Chin. Phys. Lett.

2004, Vol. 21

Issue (9): 1681-1684 DOI:

Original Articles

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

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LIU Xue-Shen, CHI Yu-Hua, DING Pei-Zhu 2004 Chin. Phys. Lett. 21 1681-1684

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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.

Keywords: 02.70.-c 03.65.Ta

Published: 01 September 2004

PACS:	02.70.-c	(Computational techniques; simulations)
	03.65.Ta	(Foundations of quantum mechanics; measurement theory)

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https://cpl.iphy.ac.cn/ OR https://cpl.iphy.ac.cn/Y2004/V21/I9/01681

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