From page 46 of "Modern Quantum Mechanics, revised edition", by J.J. Sakurai.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Sakurai: Page 46

**Physics Forums | Science Articles, Homework Help, Discussion**