Why is the most probable energy different from the speed?

[vanhees71]

The complete solution is in #13. I still don't know, what else you need.

 

[JohnnyGui]

The complete solution is in #13. I still don't know, what else you need.

Never mind, I figured it out, thanks. My calcuations in post #30 are wrong, I didn't pay attention when doing them. I was overlooking the fact that the relation between $dE$ and $dv$ is a function of $v$ while the probability itself is also a function of $v$. If the relation between $dE$ and $dv$ were a constant, then then $E_{max}$ would correspond to $v_{max}$ .

Is there actually a mathematical way to explain why the maximum probability density in terms of energy $E_{max}$ is exactly half the energy that corresponds to $v_{max}$?

 

[PeterDonis]

I figured it out, thanks.

It doesn't look like it, since you come right back with the same question:

Is there a mathematical way to explain why the maximum probability density in terms of energy $E_{max}$ is exactly half the energy that corresponds to $v_{max}$?

The math has already been discussed quite sufficiently in this thread. I think the discussion has run its course.

Thread closed.