PT对称的非厄米势对一维线性谐振子能谱的影响

Influence of energy spectra of one-dimensional linear harmonic oscillator in a non-hermitian potential with PT-symmetry

近年来,PT对称的非厄米系统由于其独特的物理性质而得到了诸多领域中研究者的广泛关注.在量子力学教学中除阐明量子力学的基本概念和物理图像外,很有必要适当引入相关的研究进展.选取一维线性谐振子体系,讨论了附加势能λ(ix)^(k)对其能谱的影响.利用微扰理论计算了体系的二级近似能谱,发现该势能在改变体系能谱方面有特殊作用,能量修正随k的变化围绕谐振子能量原值振荡,且当λ较大时可能出现能级交错的现象.该研究有助于加深对量子力学中基础和前沿知识的融合与理解.

In recent years,PT-symmetric non-hermitian systems have received widespread attention from researchers in various fields due to their unique physical properties.In the teaching of quantum mechanics,it is necessary to properly introduce relevant research progress in addition to elucidating the basic concepts and physical images of quantum mechanics.It was studied of the impacts of the PT-symmetric potentials λ(ix)^(k) on the energy spectra of one-dimensional linear harmonic oscillator systems.By solving the energy spectra with the help of perturbation theory,and it is find that this potential plays special roles changing the energy spectra.Namely,the value of the energy correction fluctuates around its original value following the change of k,as a result,the energy level overlap can be observed when λ is high enough.It can be believed that these results are helpful in understanding the basis and the frontier knowledge of quantum mechanics.