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timn
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Future of a particle in a box -- I'm fundamentally confused
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?
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.
Homework Statement
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?
Homework Equations
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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