若干 delta 势的薛定谔方程的傅里叶变换求解

熊路淋, 谭 鑫, 罗 光

doi:10.16854 / j.cnki.1000-0712.210075

大学物理 >

2021 , Vol. 40 >Issue 10: 22

DOI: https://doi.org/10.16854 / j.cnki.1000-0712.210075

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若干 delta 势的薛定谔方程的傅里叶变换求解

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重庆师范大学物理与电子工程学院，重庆 401331

熊路淋( 1999—) ，女，重庆万州人，重庆师范大学物理与电子工程学院 2020 级硕士研究生.

收稿日期: 2021-02-16

修回日期: 2021-05-21

网络出版日期: 2021-10-15

基金资助

国家自然科学基金项目青年科学基金( 11404046) ; 重庆市科委自然科学基金( cstc2012jjA50018) ; 重庆师范大学国家基金预研项目( 16XYY31) 资助

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Solving Schrödinger equations with multiple delta potentials by Fourier transformation

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College of Physics and Electronic Engineering，Chongqing Normal University，Chongqing 401331，China

Received date: 2021-02-16

Revised date: 2021-05-21

Online published: 2021-10-15

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摘要

若干 delta 势约束下的薛定谔方程的求解问题，求解过程往往很繁琐.本文研究基于傅里叶变换法求解了若干 delta势作用下的定态薛定谔方程.首先针对单 delta 势约束下的薛定谔方程进行讨论，然后讨论双 delta 势下的方程的求解，进而讨论三 delta 势的方程的求解，最后分别针对奇数个和偶数个 delta 势阱讨论了若干 delta 势约束下的薛定谔方程的求解问题.

关键词： 傅里叶变换; delta 势; 双 delta 势; 多 delta 势

本文引用格式

熊路淋, 谭鑫, 罗光 . 若干 delta 势的薛定谔方程的傅里叶变换求解[J]. 大学物理, 2021 , 40(10) : 22 . DOI: 10.16854 / j.cnki.1000-0712.210075

Abstract

The process of solving the Schrödinger equation with delta potentials is very

complicated. In this pa- per，the Fourier transform method is used to solve the Schrödinger equation

under the action of several delta poten- tials. Firstly，the Schrödinger equation with single delta

potential well is discussed，then the solution of the equation with double delta potentials is

studied. Furthermore，the solution of the equation of triple delta potentials is de-

duced. Finally，the problem of solving the Schrodinger equation under mutiple delta

potentials constraints is dis- cussed through odd and even delta potentials respectively.

Key words： Fourier transform; delta potential; double delta potentials; mutiple delta potentials

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