Position of particle in infinite potential well

[Froskoy]

Homework Statement

For the case n=1, calculate the probability that the particle is found in within the region a/4<x<3a/4 (n is the energy level, a is the width of the infinite potential well). Compare this result with the case n=8 and with the classical result.

Homework Equations

Schrödinger equation.

The Attempt at a Solution

I've calculated the probabilities for n=1 and n-8 by integrating the square of the probability amplitude over the required region. I'm totally confused by comparing it to the classical result, though. I'm not sure what this is asking? Classically, would there be an equal probability of finding the particle anywhere, so this would just be 0.5?

 

[vela]

That's right. Classically, the probability is 1/2.

 

[Froskoy]

Why? Please can you point me to somewhere that explains how this situation is modeled classically?