1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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 :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Bra & Ket notation in quantum physics
  1. Bra-ket notation (Replies: 1)

  2. Quantum bra/ket problem (Replies: 14)

Loading...