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Sakurai Modern Quantum Mechanics (Second Edition) Eq. 1.7.15

  • #1

Homework Statement


Reading Sakurai I cannot see how he gets to the end of 1.7.15 as below:

Homework Equations


dx'|x'><x'-dx' |α>
= ∫dx'|x'>{<x' |α>-Δx'∂/∂x'<x' |α>}

The Attempt at a Solution


I tried a Taylor expansion but cannot see how this is derived.
 

Answers and Replies

  • #2
blue_leaf77
Science Advisor
Homework Helper
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That's indeed a Taylor expansion, truncated up to the first order. The author wants to express the shifted position eigenket as in terms of infinitesimal change.
 
  • #3
Thank you for your reply, it has helped me understand manipulation of bra-kets.
 

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