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狄拉克符号或狄拉克标记(英语:Dirac notation)是量子力学中广泛应用于描述量子态的一套标准符号系统。在这套系统中,每一个量子态都被描述为希尔伯特空间中的态向量,定义为右矢(ket):
;每一个右矢的共轭转置定义为其左矢(bra);换一种说法,右矢的厄米共轭(即取转置运算加上共轭复数运算),就可以得到左矢。
此标记法为狄拉克于1939年将“bracket”(括号)这个词拆开后所造的。[1]在中国方面,一些旧有的教科书和文献中也将其译为“刁矢”和“刃矢”、或“彳矢”和“亍矢”,现已弃用。
矩阵表示
右矢与左矢可分别用N×1阶和1×N阶矩阵表示为:


不同的两个态矢量的内积则由一个括号来表示:
,当狄拉克符号作用于两个基矢时,所得值为:
(
为克罗内克函数)
相同的态矢量内积为:
。
参考文献
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