Bra-ket Notation and Operator

  • Thread starter rsaad
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  • #1
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Hi
If C is an operator such that C|1> = |1> and C|2>=|2>, then C^3 |1>= |1>|1>|1> =|1> ^ 3 ? If yes, then what does this C^3 represent?
:confused:
 

Answers and Replies

  • #2
I like Serena
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Hi
If C is an operator such that C|1> = |1> and C|2>=|2>, then C^3 |1>= |1>|1>|1> =|1> ^ 3 ? If yes, then what does this C^3 represent?
Welcome to PF, rsaad!

If f is a function such that f(x)=x.
And f3(x) denotes f(f(f(x))).
What is f3(x)?
 
  • #3
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OMG! That makes sense! Thank you soooo much!!!!
 
  • #4
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f^3 x is a function again =)
 
  • #5
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You're welcome. :wink:

f^3 x is a function again =)
Yeah... which function?

And is C^3 |1> = |1>|1>|1>?
 
  • #6
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No. it is just |1>
 
  • #7
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So that's an identity function
 
  • #8
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Right!
 
  • #9
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Your C is not the identity function!
Try to calculate C^3 |2> to see the difference.

Edit: Ignore that post, see below.
 
Last edited:
  • #10
I like Serena
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Your C is not the identify function!
Try to calculate C^3 |2> to see the difference.
C^3 |2> = C C C |2> = C C |2> = C |2> = |2>

Where is the difference?
 
  • #11
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Oh sorry, I somehow read C |2> = 2 |2> in the first post. You are right.
Ok, it might be the identity function (but we cannot be sure based on 2 examples only).
 
  • #12
Fredrik
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The notation |1>|1>|1> doesn't make sense here.
 
  • #13
dextercioby
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There's no such thing as the 3rd or any power of a vector.
 

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