# Fock states and eigenstates

1. May 18, 2010

### Ylle

1. The problem statement, all variables and given/known data

I have to show that the Fock states are eigenstates for the operators ${{\hat{a}}^{\dagger }}$ and/or ${\hat{a}}$

And I'm not totally sure how to show this.

2. Relevant equations

?

3. The attempt at a solution

I know that if I use the operators on a random Fock state i get:

$$a^{\dagger}|n\rangle=\sqrt{n+1}|n+1\rangle$$
$$a|n\rangle=\sqrt{n}|n-1\rangle$$

So what's next ?

Regards

2. May 18, 2010

### nickjer

Are you sure you are typing the question correctly? Because as you just showed, Fock states are not eigenstates of the creation and annihilation operators. Maybe you are getting it confused with coherent states.

3. May 18, 2010

### Ylle

Ahhh...
It said: IS the Fock states eigenstates for the operators, doh...

So when I use the operators on the Fock state, they are not eigenstates because of the |n-1> and |n+1> at the end, which should have been just |n> in each case, or am I way off ?

4. May 18, 2010

### nickjer

Yes, an eigenstate of an operator won't change under an operation on the operator. So you would just get back |n> with a coefficient called the eigenvalue.

5. May 18, 2010

### Ylle

Well, thank you :)
Didn't know it was that easy.