氢原子圆轨道对三维径向位置和径向动量不确定度的探究  

Theoretical exploration of uncertainty in three-dimensional radial position and radial momentum using the circular orbit of hydrogen atoms

作　　者：孙华洋 陈理想[1] SUN Hua-yang;CHEN Li-xiang(College of Physics,Xiamen University,Xiamen,Fujian 361005,China)

机构地区：[1]厦门大学物理学系,福建厦门361005

出　　处：《大学物理》2024年第7期6-10,共5页College Physics

基　　金：高等学校教学研究项目(NO.DWJZW202223hd);国家自然科学基金重点项目(12034016)资助。

摘　　要：在直角坐标系中,线位置和线动量满足不确定性关系,ΔxΔp≥h/2.而关于径向位置和径向动量是否满足类似的不确定关系式是近年来的研究热点之一,其中的关键是如何构建一个满足自伴随条件的径向算符.在二维双曲动量算符的启发下,本文从理论上研究了三维双曲动量算符与径向位置对数满足的不确定关系.以氢原子为例,计算了不同圆轨道所对应的径向位置对数及三维双曲动量的不确定度的乘积形式,Δln rΔP_(H),并发现了随着主量子数的增大,圆轨道波函数与智慧态之间的逼近关系.In a Cartesian coordinate system,linear position and linear momentum satisfy the uncertainty relationship,ΔxΔp≥h/2.Recent years also witnessed the research interest as to whether the radial position and radial momentum satisfies the similar uncertain relationship,in which one of the key points is how to construct a radial operator that satisfies the self-adjoint condition.Here,inspired by the two-dimensional hyperbolic momentum operator,we theoretically study the uncertainty relationship between the three-dimensional hyperbolic momentum operator and the radial position logarithm.Taking hydrogen atoms as an example,the products of the uncertainty of radial position logarithmic and that of three-dimensional hyperbolic momentum,i.e.,Δln rΔP_(H),for different circular orbits are calculated.It is found that as the main quantum number increases,the wavefunctions of circular orbits are more approaching to the intelligent states.

关 键 词：三维双曲动量 氢原子 海森伯不确定性原理 智慧态 

分 类 号：O4-1[理学—物理]