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Sakurai Modern Quantum Mechanics (Second Edition) Eq. 1.7.15

  1. Jun 20, 2016 #1
    1. The problem statement, all variables and given/known data
    Reading Sakurai I cannot see how he gets to the end of 1.7.15 as below:

    2. Relevant equations
    dx'|x'><x'-dx' |α>
    = ∫dx'|x'>{<x' |α>-Δx'∂/∂x'<x' |α>}
    3. The attempt at a solution
    I tried a Taylor expansion but cannot see how this is derived.
     
  2. jcsd
  3. Jun 20, 2016 #2

    blue_leaf77

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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.
     
  4. Jun 23, 2016 #3
    Thank you for your reply, it has helped me understand manipulation of bra-kets.
     
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