What does the operator C^3 represent in Bra-ket notation?

[rsaad]

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?

 

[I like Serena]

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)?

 

[rsaad]

OMG! That makes sense! Thank you soooo much!

 

[rsaad]

f^3 x is a function again =)

 

[I like Serena]

You're welcome.

f^3 x is a function again =)

Yeah... which function?

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

 

[rsaad]

No. it is just |1>

 

[rsaad]

So that's an identity function

 

[I like Serena]

Right!

 

[mfb]

Your C is not the identity function!
Try to calculate C^3 |2> to see the difference.

Edit: Ignore that post, see below.

 

[I like Serena]

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]

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]

The notation |1>|1>|1> doesn't make sense here.

 

[dextercioby]

There's no such thing as the 3rd or any power of a vector.