What's the Probability of Finding a Quantum Particle in Each Box?

[Axiom17]

Homework Statement

A quantum particle is described by the wavefunction $\psi(r)$. There are 2 identical boxes (A & B).. what's the probability of finding the particle in each box?

Homework Equations

$$\psi(r)= \left\{ {\begin{array}{ll}<br /> <br /> 1+i & if A\\<br /> 1-i & if B\\<br /> 0 & if elsewhere\\<br /> <br /> \end{array}} \right$$

The Attempt at a Solution

I'm really not sure where to start with this I see that I have the wavefunction $\psi$ for each box (and elsewhere), but I'm not sure what to do as far as the calculations.. hopefully just need a bit of a hint to get me going with it.

 

[Theaumasch]

Sorry, but I don't know how to use Latex, so please try to follow what I think:

|psi|² is the probability density, let's call it P1 for the first box, P2 for the second en P3 for the third.

P1=(1-2i)(1+2i)=5
P2=(1-i)(1+i)=2
P3=(1+i)(1-i)=P2=2

Because the probability is normalized, we have to divide by P1+P2+P3=9 to get p1, p2 and p3. This gives that the probability p2 to find it in the second box is 2/9.

 

[Axiom17]

Ok thanks for that I get it now