傅里叶变换求解一维PT对称delta势阱中的束缚态  

Solving bound states in one-dimensional PT symmetric delta potential using Fourier transform

作　　者：贾春玉 梁兆新 JIA Chun-yu;LIANG Zhao-xin(Department of Physics,Zhejiang Normal University,Jinhua,Zhejiang 321004,China)

机构地区：[1]浙江师范大学物理系,浙江金华321004

出　　处：《大学物理》2024年第7期3-5,15,共4页College Physics

基　　金：浙江省自然科学基金重点项目(LZ21A040001);国家自然科学基金(12074344)资助。

摘　　要：具有PT对称性的系统是量子力学研究前沿热点.一维PT对称delta势阱中束缚态问题是PT系统最简化模型,对其精确求解是具有科研价值的教学问题.本文通过求解一维PT对称delta势的定态薛定谔方程研究了PT对称性对系统束缚态以及本征能量的影响.首先,采用傅里叶变换对一维PT对称delta势的定态薛定谔方程进行了求解并讨论.其次,通过数值手段确定了一维PT对称delta势阱中束缚态的轮廓以及系统的本征能量.最后,分析和探讨了PT对称势强度与本征能量的关系.本文把量子力学教学中传统的厄米delta势阱本征值问题扩展到非厄米delta势阱问题,是对量子力学教学必做习题的有益且及时地扩展.Systems with PT symmetry are a hot topic in quantum mechanics research.The bound state problem in one-dimensional PT-symmetric delta potential well is the most simplified model of PT system,and its exact solution is a teaching problem with scientific research value.In this work,the effect of PT symmetry on the bound state and the intrinsic energy of a system is studied by solving the stationary Schr dinger equation of one-dimensional PT-symmetric delta potential.Firstly,the stationary Schr dinger equation of one-dimensional PT-symmetric delta potential is solved and discussed by Fourier transform.Secondly,the contours of the bound states and the intrinsic energies of the system are determined by numerical means.Finally,the relationship between PT symmetry potential strength and intrinsic energy is analyzed and discussed.In this paper,the traditional Hermitian delta potential well eigenvalue problem is extended to non-Hermitian delta potential well problem,which is a useful and timely extension of the necessary exercises in quantum mechanics teaching.

关 键 词：PT对称 delta函数势 傅里叶变换 非厄米量子力学 

分 类 号：O4-1[理学—物理]