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Quick question about bra-ket notation

  1. Jan 21, 2014 #1
    1. The problem statement, all variables and given/known data

    On Wikipedia there is an article about perturbation theory. To understand something I need to understand the following relation. They say:

    2. Relevant equations

    [itex]H |n> = E_n |n>[/itex]

    So:

    [itex]<n| H = <n| E_n[/itex]

    H is Hermitian.

    So: Why is this?

    3. The attempt at a solution

    I don't know if this is valid.

    [itex](H \cdot |n>)^\dagger = (E_n \cdot |n>)^\dagger[/itex]

    [itex]\Leftrightarrow[/itex]

    [itex]<n| H^\dagger = <n| E_n^\dagger[/itex]

    And since H is Hermitian and E_n is real, I get:

    [itex]<n| H = <n| E_n[/itex]

    Is this how things work?
     
  2. jcsd
  3. Jan 21, 2014 #2

    DrClaude

    User Avatar

    Staff: Mentor

    That looks correct.
     
  4. Jan 21, 2014 #3
    Looks fine to me too.
     
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