Quantum Mechanics "Expectation"

roshan2004

1. The problem statement, all variables and given/known data
1. Calculate the expectation value [tex]<p_{x}>[/tex] 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.


2. Relevant equations
[tex]\psi _{n}=\sqrt{\frac{2}{L}}sin \frac{n\pi x}{L}[/tex]
[tex]<p_{x}>=\int \psi^*p_{x}\psi dx[/tex]
[tex]<x>=\int \psi^*x\psi dx[/tex]


3. 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.