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Bra & Ket notation in quantum physics

  1. Aug 19, 2013 #1
    1. The problem statement, all variables and given/known data

    If |A> = x |B> + y |C> where |B> and |C> are orthonormal, then what happens when <A|A> ?

    3. The attempt at a solution

    Would <A| = x* <B| + y* <C|?

    I'm not really sure where to go from there
    Last edited: Aug 19, 2013
  2. jcsd
  3. Aug 19, 2013 #2


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    hi blueink! welcome to pf! :smile:

    now expand (x* <B| + y* <C|)(x |B> + y |C>) :wink:

    [and what is <B||B>? what is <B||C>?]
  4. Aug 19, 2013 #3


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    Write down <A|A> with your <A|, and use the distributive property of the scalar product:
    <X| (|Y>+|Z>) = <X|Y> + <X|Z>
    Afterwards, simplify.
  5. Aug 19, 2013 #4
    Expanding (x* <B| + y* <C|)(x |B> + y |C>)
    =(x* <B|)(x |B>)+(x* <B|)(y |C>)+(y* <C|)(x |B>)+(y* <C|)(y |C>)
    =x*x <B|B> + x*y <B|C> + y*x <C|B> + y*y<C|C>

    Where <B|B> and <C|C> = 1 and <B|C> and <C|B> = 0?
  6. Aug 19, 2013 #5


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    yup! :smile:

    that's what's so beautiful about orthonormal systems! :wink:

    (erm … you did mean orthonormal, and not just orthogonal? :redface:)
  7. Aug 19, 2013 #6
    I did mean orthonormal, ahh confusion! thanks :)
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