What is the expectation value of ψ = x3 when 0≤ x ≤a and 0 otherwise?

[leroyjenkens]

Homework Statement

ψ = x³ when 0≤ x ≤a and 0 otherwise
find <x>

Homework Equations

∫ψ*ψdx=1

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.

 

[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.

 

[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.