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From page 46 of "Modern Quantum Mechanics, revised edition", by J.J. Sakurai.
In equation (1.6.24),
[tex] \left[\mathbf{x}, \mathcal{T}(d\mathbf{x'}) \right] = d \mathbf{x'} \mid \mathbf{x'} + d \mathbf{x'} \rangle \approx d \mathbf{x'} \mid \mathbf{x'} \rangle [/tex]
It is written: "where the error made in writing the last line of (1.6.24) is of second order in [itex]d \mathbf{x'}[/itex]". How does that happen? From a Taylor expansion of [itex]\mid \mathbf{x'} + d \mathbf{x'} \rangle [/itex] ? If so, how do you Taylor expand a ket?
In equation (1.6.24),
[tex] \left[\mathbf{x}, \mathcal{T}(d\mathbf{x'}) \right] = d \mathbf{x'} \mid \mathbf{x'} + d \mathbf{x'} \rangle \approx d \mathbf{x'} \mid \mathbf{x'} \rangle [/tex]
It is written: "where the error made in writing the last line of (1.6.24) is of second order in [itex]d \mathbf{x'}[/itex]". How does that happen? From a Taylor expansion of [itex]\mid \mathbf{x'} + d \mathbf{x'} \rangle [/itex] ? If so, how do you Taylor expand a ket?
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