# Finding expectation value

1. Jan 8, 2014

### leroyjenkens

1. The problem statement, all variables and given/known data
ψ = x3 when 0≤ x ≤a and 0 otherwise
find <x>

2. Relevant equations
∫ψ*ψdx=1

3. The attempt at a solution
So first I multiplied x3 times A, to get Ax3, then plugging that into the equation, I get ∫A2x6dx=1
Then I solve that for A, getting A = $$\sqrt{\frac{7}{a^{7}}}$$
So I plug that value back into my integral in place of A and since I'm solving for the expectation value <x>, I plug x into that equation too? This is confusing.

2. Jan 8, 2014

### maajdl

You have succefully normalised the wavefunction: with the A value that you calculated, the (total) probability of finding the particle anywhere is 1.
You still need now to calculate <x> = ∫ψ* x ψ dx .

You should find something between 0 and a, and closed to a than to 0.

3. Jan 8, 2014

### leroyjenkens

I'm sort of confused on what to plug in for ψ and ψ* in that equation. Ax3 for both? In that case, I get (7/8)a. That seems a little high. Thanks.