Creation and Annihilation Operators

[jhosamelly]

We know that

a|n> = √n | √(n-1)>

and

a' |n> = √(n+1) | n + 1 >

so, If we use this to find

<n|a'a|n>

it would be equal to n

<n|a'a|n> = n

Am I correct?

I'm not really sure about my calculations.

I operate with a first so.

<n|a'a|n>
<n|a' √n | √(n-1)>

= n

?

Can someone please help me with the complete solution?

 

[mfb]

<n|a'a|n> = <n|a' √n | (n-1)> (no square root for the state)
= √n <n|a' | (n-1)> (√n is a scalar, you can pull it out)
= √n <n|√n | n>
= √n √n <n|n>
=n

 

[jhosamelly]

Thanks yah no √ for the state. Sorry.