Position of particle in infinite potential well

AI Thread Summary
The discussion focuses on calculating the probability of finding a particle in an infinite potential well for energy levels n=1 and n=8 within the region a/4<x<3a/4. The user successfully integrated the probability amplitude to find these probabilities but is confused about comparing them to the classical result. Classically, the probability of finding the particle in that region is 0.5, as it assumes equal likelihood across the well. The user seeks clarification on how classical modeling leads to this probability. Understanding the classical model's assumptions is essential for making the comparison clear.
Froskoy
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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?
 
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That's right. Classically, the probability is 1/2.
 
Why? Please can you point me to somewhere that explains how this situation is modeled classically?
 
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