(adsbygoogle = window.adsbygoogle || []).push({}); Future of a particle in a box -- I'm fundamentally confused

1. The problem statement, all variables and given/known data

A particle is somewhere in the right half of a one-dimensional infinite potential well with sides at x=-a/2 and x=a/2. The particle's wave function is constant over x, i.e.

[tex]\psi(x) = \sqrt{2/a}[/tex]

for 0<x<a/2 and zero for all other x.

Will the particle remain localized at later times?

2. Relevant equations

3. The attempt at a solution

I don't even understand the question. How could you call this particle localized, when all we know about its position is a probability function? Does "remain localized" mean that the probability function doesn't change, or that we know how it will change?

What would happen with the particle if it was just left there? Would the wave function change, and if so, why?

A "free" particle in a box has the wave function http://en.wikipedia.org/wiki/Particle_in_a_box#Wavefunctions" -- why doesn't this one? Is it because we already have some information on its position?

Sorry if the questions are many.

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# Future of a particle in a box - I'm fundamentally confused

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