Does the Correspondence Principle Confirm Equal Probability in Quantum Systems?

[nargle]

Homework Statement

For a particle in a one-dimensional box of length a, I am attempting to find the probability that the particle will be located between 0 and a/4, in the limit of large quantum numbers.

Homework Equations

The Correspondence Principle states that quantum mechanical systems may be described by classical physics in the limit of large quantum numbers.

The Attempt at a Solution

I understand that classically the particle has an equal probability of being anywhere in the box. So, by the Correspondence Principle for large quantum numbers the particle also has an equal probability of being found anywhere in the box. Assuming a normalized wavefunction, the probability of the particle being between 0 and a is 1. Then, am I correct in thinking that the probability of the particle being between 0 and a/4 is 1/4?

Thanks.

 

[tiny-tim]

Welcome to PF!

Hi nargle! Welcome to PF!

For a particle in a one-dimensional box of length a, I am attempting to find the probability that the particle will be located between 0 and a/4, in the limit of large quantum numbers.

… am I correct in thinking that the probability of the particle being between 0 and a/4 is 1/4?

Yup!

 

[nargle]

Thanks tiny-tim!