【摘要】 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。更多还原

【Abstract】 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.更多还原