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Simple dirac notation problem

  1. Nov 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Imagine you have two vectors |a> and |b> such that:
    |c> = |a> + |b>

    Now imagine you want the dot product:


    Is that the same as:

    <c|a> = [ <a|*+<b|* ] |a> = <a*|a> + <b*|a>

    where * represents the complex conjugate of the vector?

    2. Relevant equations

    3. The attempt at a solution~

    Thanks in advance for any answer.

  2. jcsd
  3. Nov 3, 2012 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    You'd not normally put the star outside the bra like that.
    if a is a state then |a> is the state vector corresponding to wavefunction Ya ... we may sometimes write |Ya> when you are starting out.

    ##<\psi_a|\psi>= \int \psi_a^\star \psi##

    (I'm hoping someone else can do a better job of this explanation. :/ )
    BTW: you know your vector |c> is not normalized right?
  4. Nov 3, 2012 #3
    Yes, I'm aware that |c> is not normalized, but in this case it doesn't matter. I'm just learning the math behind Dirac's notation. I am not yet working with state vectors or anything of that kind.
    Thanks for your answer!
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