- #1

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## Homework Statement

This isn't a homework problem. I am reading Sakurai (Modern Quantum Mechanics) and came upon this:

We must therefore have anoperator identity

[tex]\left[\textbf{x},\hat{T}\left(d\textbf{x}'\right)\right]=d\textbf{x}'[/tex] (1.6.25)

or

[tex]-i\textbf{xK}\cdot d\textbf{x}'+i\textbf{K}\cdot d\textbf{x}'\textbf{x}=d\textbf{x}'[/tex] (1.6.26)

## The Attempt at a Solution

When I work that out:

[tex]\left[\textbf{x},\hat{T}\left(d\textbf{x}' \right)\right]=\textbf{x}\left(1-i\textbf{K}\cdot d\textbf{x}' \right)-\left(1-i\textbf{K}\cdot d\textbf{x}' \right)\textbf{x}[/tex]

[tex]=-i\textbf{xK}\cdot d\textbf{x}'+i\textbf{K}\cdot d\textbf{x}'\textbf{x}[/tex]

[tex]=i\left(\textbf{K}\cdot d\textbf{x}'\textbf{x}-\textbf{xK}\cdot d\textbf{x}' \right)[/tex]

[tex]=d\textbf{x}'[/tex]

I'm not seeing how they get [tex]d\textbf{x}'[/tex] out of that.