Where Is the Average Position of a Particle in a Box?

[andresordonez]

SOLVED
(Example 6.15 from Modern Physics 3e- Serway)

Homework Statement

Compute the average position <x> for the particle in a box assuming it is in the ground state

Homework Equations

$$|\Psi|^2=(2/L)\sin^2{(\pi x/L)}$$
$$<x> = \int^{x_0+L}_{x_0}x|\Psi|^2dx$$

The Attempt at a Solution

$$<x>=x_0+L/2-\frac{L}{2\pi}\sin{\frac{2\pi x_0}{L}}$$

I'm pretty sure this is the answer, however, I don't understand why I get that last term, I mean, the average position should be $$x_0 + L/2$$ right?

If I take $$x_0=0$$ then the answer is what I was hoping for (Indeed this is the original procedure in the book), but in the more general expression with $$x_0 \neq 0$$ I get the previous answer.

 

[Galileo]

If you take the well with $x_0$ at the left side, then your wavefunction should also be shifted with respect to the solution for $x_0=0$.

You're missing $x_0$in the expression for the wavefunction.

 

[andresordonez]

right! Thanks.