# Find wavefunctions given states

## Homework Statement

Given state: |ψ> = |0> + α|1> + σ^2/√2 |2>

find the wavefunctions.

I am confused between states and wavefunctions, everywhere ive read it says that state (ie the wavefuctions), really need some enlightenment here..

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gabbagabbahey
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## Homework Statement

Given state: |ψ> = |0> + α|1> + σ^2/√2 |2>

find the wavefunctions.

I am confused between states and wavefunctions, everywhere ive read it says that state (ie the wavefuctions), really need some enlightenment here..
Can you post the entire problem statement verbatim (word for word) as it is given to you?

Consider the two states of the electro-magnetic field

|ψ> = |0> + α|1> + σ^2/√2 |2>
ρ = 3/8((|0>+|1>(<0|+<1|)) + 1/4 |0><0|

where |n>, n= 0, 1, 2 are Fock states

find the photon number distributions and the wavefunctions for the two states

So i understand for the second state there wouldn be any wavefunctions as it is a mixed state.

The first state however is a pure state, so i went like x|ψ> . But after that im stuck, any hints so that i can continue?

gabbagabbahey
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Gold Member
So i understand for the second state there wouldn be any wavefunctions as it is a mixed state.

The first state however is a pure state, so i went like x|ψ> . But after that im stuck, any hints so that i can continue?
What do you mean the second state? $\hat{\rho}$ is the density matrix, not a state.

Eh I think it's confusing with the notations used in the question.. But it isint the density matrix... Just a mixed state

gabbagabbahey
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Gold Member
Eh I think it's confusing with the notations used in the question.. But it isint the density matrix... Just a mixed state
Technically, it's the density matrix that describes the mixed state. The state cannot be represented by a wavefunction (unless you include an additional random phase variable, which, if you haven't learned about in class, you probably needn't worry about), but you can still find the photon number distributions. Have you done that?

It seems odd to me to ask for the wavefunctions of the two states, especially without specifying a basis, maybe I'm just not seeing the point of the question. Hopefully someone else will weigh in here.