# Bra-ket Notation and Operator

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?

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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?

If f is a function such that f(x)=x.
And f3(x) denotes f(f(f(x))).
What is f3(x)?

OMG! That makes sense! Thank you soooo much!!!!

f^3 x is a function again =)

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You're welcome.

f^3 x is a function again =)

Yeah... which function?

And is C^3 |1> = |1>|1>|1>?

No. it is just |1>

So that's an identity function

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Right!

mfb
Mentor
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:
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?

mfb
Mentor
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).

Fredrik
Staff Emeritus