Proving the expectation value of any eigenvalue function

[Cocoleia]

Homework Statement

Homework Equations

The Attempt at a Solution

When I take the second formula, multiply by it's conjugate and then by x and do the integral of the first formula, I get 0, and not L/2, for <x>. Am I missing a formula ?
The complex conjugate of the exponential part multiplied by the exponential part simplifies to 1, and when I do the integral I end up with 0.

 

[kuruman]

What are your integration limits?

 

[Cocoleia]

What are your integration limits?

-infinity and +infinity, as in the first formula (the orange background)

 

[kuruman]

What is the size of the "box" the particle is in?

 

[Cocoleia]

What is the size of the "box" the particle is in?

L? so would it be from 0 to L ?

 

[kuruman]

Right. The particle is confined from 0 to L.