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Cogswell
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Homework Statement
The needle on a broken car speedometer is free to swing and bounces off perfectly off the pins at either end, so that if you gave it a flick it's equally likely to come to rest at 0 and ## \pi ##
What is the probability density, ## p(x) ##?
Homework Equations
[tex]\int^{\pi}_{0} p(x) dx = \int^{\pi}_{0} |\Psi (x,t)|^2 dx = 1[/tex]
The Attempt at a Solution
This may sound really dumb but I was thinking that since that it's equally likely to be from anywhere between 0 and pi, then it'll just be a straight horizontal line, p(x) = 1.
But since it has to be normalised from 0 to pi, then p(x) will just be 1/pi.
But that didn't seem right because it had to drop off to 0 at x=0 and x=pi so I was thinking of a sine curve, and maybe p(x) = sin(x)
How does that work though? It says it's equally likely to land anywhere from 0 to pi, but with a sine curve it's obvious that it'll have a way higher chance of landing in the middle...