A systematic approach for obtaining the Green functions of time-dependent Schr�dinger equations by Fourier transform

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/103986

Title:	A systematic approach for obtaining the Green functions of time-dependent Schr�dinger equations by Fourier transform
Authors:	汪治平;Tsaur, Gin-yih;Wang, Jyhpyng
Contributors:	理學院物理學系
Keywords:	Fourier transform;Green function;time-dependent Schr�dinger equation
Date:	2016-05-10
Issue Date:	2026-04-23 11:41:18 (UTC+8)
Publisher:	IOP Publishing Ltd.;IOP Publishing
Abstract:	摘要： The Green function method is a powerful technique for solving the initial value problem in quantum mechanics. Once the Green function is solved the whole wavefunction evolution is represented in a concise form and can be evaluated conveniently by numerical integration. We present a method for constructing the Green functions systematically which is different from the conventional methods of eigenfunction expansion or path integration. By using variable changing, function substitution, and Fourier transforms, the time dependent Schrödinger equations can be simplified and the solutions for the simplified equations can be easily derived. We then obtain the Green functions for the original equations by the reverse transforms. The method is demonstrated for the linear potential, the harmonic oscillator, the centrifugal potential, and the centripetal barrier oscillator, where the Green function for the centripetal barrier oscillator has not been solved previously by conventional methods. The method and examples illustrated in this paper can be utilised to strengthen undergraduate courses on quantum mechanics and/or partial differential equation. 其他題名： EJP 其他題名： Eur. J. Phys 出版者： IOP Publishing 出版日期： 2016-07-01 出處： European journal of physics, 2016-07, Vol.37 (4), p.45402 資源來源： Institute of Physics Journals 版權： 2016 IOP Publishing Ltd 識別號： ISSN: 0143-0807 識別號： EISSN: 1361-6404 識別號： DOI: 10.1088/0143-0807/37/4/045402 識別號： CODEN: EJPHD4
Appears in Collections:	[Department of Physics] journal & Dissertation

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