无量纲量子力学态矢表示

Dimensionless quantum mechanical state vector

狄拉克基于叠加原理的要求引入了物理状态的矢量表示,仓促间留下了量纲不一致的问题。近年有研究者从量纲分析的角度做了弥补,但未涉及问题的实质。本文坚持量子力学态矢量应采用无量纲表示,从而做到量子力学表示中波函数、变换、物理量算符及其本征值等角色主体各自的量纲一致性,特别是使得态空间上的变换满足群的要求。基于湮灭算符和产生算符a,a+可为位置算符、动量算符构建无量纲态矢表示,消除文献中不自洽的量纲关系所造成的一些困扰。

Starting from the superposition principle,Dirac introduced complex vector space representation for quantum mechanics,leaving behind in a hash some flaws in the theory,in particular dimension discrepancy concerning the basis vector sets{|x}and{|p}for position operator and momentum operator,respectively.A remedy for this discrepancy was recently proposed by assigning dimension to the state vectors|x and|p,which is unacceptable and may bring with new confronts.Abiding by the principle of dimensionless representation for state vectors,and thus the relevant transformations,we formulate a dimensionless representation for the state vectors for position and momentum,i.e.,|q and|p,by using the annihilation and creation operators a,a+,thus eliminate the problems caused by dimension discrepancy in quantum mechanics literature.