I am reading the book by J.J.Sakurai, in chaper 3, there is a relation given as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\langle \alpha', jm|J_z A |\alpha, jm\rangle[/tex]

Here, j is the quantum number of total angular momentum, m the component along z direction, [tex]\alpha[/tex] is the third quantum number. [tex]J_z[/tex] is angular momentum operator, A is arbritary operator. Generally, [tex]J_z[/tex] is not commutate with A, but Sakurai just give the result directly as following

[tex]m\hbar\langle \alpha', jm|A|\alpha, jm\rangle[/tex]

As you see, this just like have [tex]J_z[/tex] acting on the bar and returns the [tex]m\hbar\langle \alpha', jm|[/tex]. My question is: how can [tex]J_z[/tex] acting on the bar vector?

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# Question about commutation and operator

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