Is Braket Operation Legal? Elaborate Here

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intervoxel
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Is this operation legal?

[itex]\langle A_1|BA|A_2\rangle=A_2\langle A_1|B|A_2\rangle[/itex]

If so, please elaborate on that.

Thanks.
 
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If [itex]|A_2 \rangle[/itex] is an eigenvector of the operator [itex]\mathbf{A}[/itex] with eigenvalue [itex]A_2[/itex] then your operations are correct.
 
So

[tex] \langle A_1|BA|A_2\rangle=\langle A_1|B\rangle \langle A|A_2\rangle=<br /> \langle A_1|B\rangle A_2=A_2\langle A_1|B\rangle[/tex]

right?

Thank you.
 
No. You are mixing up operators with bras and kets. It looks like A and B are supposed to be operators. If so, the expressions |A>, <A|, |B>, or <B| make no sense. Operators are neither bras nor kets.