From page 54 of 'Modern Quantum Mechanics, revised edition" by J. J. Sakurai.(adsbygoogle = window.adsbygoogle || []).push({});

Obtaining equation (1.7.15),[tex]

\begin{eqnarray}

\left(1- \frac{ip\Delta x'}{\hbar} \right) \mid \alpha \rangle & = & \int dx' \mathcal{T} ( \Delta x' ) \mid x' \rangle \langle x' \mid \alpha \rangle \\

& = & \int dx' \mid x' + \Delta x' \rangle \langle x' \mid \alpha \rangle \\

& = & \int dx' \mid x' \rangle \langle x' - \Delta x' \mid \alpha \rangle \\

& = & \int dx' \mid x' \rangle \left( \langle x' \mid \alpha \rangle - \Delta x' \frac{\partial}{\partial x'} \langle x' \mid \alpha \rangle \right)

\end{eqnarray}

[/tex]How does the last line come about? Is it a Taylor expansion?

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# Sakurai page 54: Is this a Taylor expansion?

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