What Are the Integration Limits for Calculating Expectation Values in a 1D Box?

[roshan2004]

Quantum Mechanics "Expectation"

Homework Statement

1. Calculate the expectation value $$<p_{x}>$$ of the momentum of a particle trapped in a one-dimensional box.
2. Find the expectation value <x> of the position of a particle trapped in a box L wide.

Homework Equations

$$\psi _{n}=\sqrt{\frac{2}{L}}sin \frac{n\pi x}{L}$$
$$<p_{x}>=\int \psi^*p_{x}\psi dx$$
$$<x>=\int \psi^*x\psi dx$$

The Attempt at a Solution

I got confused on choosing the limits for both the problems for integrating them. What's the limits I should chose for both the problems.

 

[Doc Al]

Where is Ψ non-zero? (What are the boundaries of the box?)

 

[roshan2004]

x=0 and x=L

 

[roshan2004]

Thanks I got it. The limits that I have to use are x=0 and x=L

 

[Doc Al]

Exactly.