- #1
madmike159
Gold Member
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I was reading part of a book which was explaining about the probability of finding a particle on a 1d line.
[tex]\int^{+\infty}_{-\infty}[/tex]P(x) dx = 1
This sounds right because if the line was infinitely long then the particle must be on it.
You can them intergrate between a and b to find the probability of it being in a length and if a and b were the same the probability would be 0.
But when you intergrate P(x) dx you get [tex]\frac{Px^{2}}{2}[/tex]
by putting the numbers in you get P[tex]\infty[/tex] - -P[tex]\infty[/tex]
or P[tex]\infty[/tex] + P[tex]\infty[/tex] = P[tex]\infty[/tex]
A probability can't be more than 1. I must be missing something or dealing with the infinities in the wrong way.
(Sorry it looks like P^infinity its P x infinity but I couldn't change it.)
[tex]\int^{+\infty}_{-\infty}[/tex]P(x) dx = 1
This sounds right because if the line was infinitely long then the particle must be on it.
You can them intergrate between a and b to find the probability of it being in a length and if a and b were the same the probability would be 0.
But when you intergrate P(x) dx you get [tex]\frac{Px^{2}}{2}[/tex]
by putting the numbers in you get P[tex]\infty[/tex] - -P[tex]\infty[/tex]
or P[tex]\infty[/tex] + P[tex]\infty[/tex] = P[tex]\infty[/tex]
A probability can't be more than 1. I must be missing something or dealing with the infinities in the wrong way.
(Sorry it looks like P^infinity its P x infinity but I couldn't change it.)