径向动量的等效算符及其量子测量

肖世发，刘全慧

收稿日期:2018-09-10 修回日期:2018-12-26 出版日期:2019-06-20 发布日期:2019-07-01
作者简介:肖世发( 1975-) ，男，贵州金沙人，岭南师范学院讲师，硕士，主要从事大学物理教学和研究工作.
基金资助:
广东省教学质量与教学改革工程项目-理工科( 2017117) ; 岭南师范学院精品课程( 114961700239) ; 岭南师范学院大学物理教学
团队项目( 114961700249) ; 岭南师范学院教学改革项目( LSJGMS1815) 资助

XIAO Shi-fa1，LIU Quan-hui2

1.School of Physics and Technology，Lingnan Normal University，Zhanjiang，Guangdong 524048，China; 2.School for Theoretical Physics，School of Physics and Electronics，Hunan University，Changsha，Hunan 410082，China

Received:2018-09-10 Revised:2018-12-26 Online:2019-06-20 Published:2019-07-01

摘要： 提出了一种在正交曲线坐标系分解动量的新方法，进而给出了球坐标下径向动量算符的一种等效表示.尽管径向动

量算符本身不能测量，这个等效算符却能测量，从而解决了径向动量的非自伴性但是具有不确定度之间的矛盾.以基态氢原子

为例，给出了等效径向动量的值的分布.

关键词: 径向动量, 几何动量, 动量分解

Abstract: A new decomposition of the momentum operator in curvilinear coordinates is proposed，from which

an equivalent operator of radial operator is resulted. Though the radial operator itself is non-self-adjoint and is not

measurable in physics，the equivalent operator is in fact the difference of two self-adjoint operators，so is measurable.

Thus，a superficial contradiction between the non-self-adjointness and existence of the uncertainty for the radial

momentum operator is resolved. What is more，the Hydrogen atom ground state is used to show how to measure

the equivalent operator.

Key words: radial momentum, geometric momentum, decomposition of momentum

肖世发, 刘全慧. 径向动量的等效算符及其量子测量[J]. 大学物理, 2019, 38(6): 4-7.

XIAO Shi-fa, LIU Quan-hui. An equivalent operator of radial operator and its quantum measurement[J]. College Physics, 2019, 38(6): 4-7.

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