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Bra & Ket notation in quantum physics

  • Thread starter blueink
  • Start date
  • #1
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Homework Statement



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


The Attempt at a Solution



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

I'm not really sure where to go from there
 
Last edited:

Answers and Replies

  • #2
tiny-tim
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Homework Helper
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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>?]
 
  • #3
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I'm not really sure where to go from there
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.
 
  • #4
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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?
 
  • #5
tiny-tim
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Homework Helper
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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:)
 
  • #6
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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:)
I did mean orthonormal, ahh confusion! thanks :)
 

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