I have a differential that depends only on [itex]\cos{\theta}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\operatorname{d}\sigma}{\operatorname{d} \Omega} = f(\cos{\theta})[/tex]

I am numerically solving this differential equation for [itex]\sigma[/itex], which physically is a cross section, for [itex]0 \leq \theta \leq \pi[/itex]. The differential contains a parameter [itex]s[/itex]. I am solving the differential for a given value of [itex]s[/itex], then incrementing this parameter and solving the differential again.

I am solving the differential over a range of [itex]s[/itex] (3 to 200), in increments of 0.1 ([itex]s[/itex] is, for the curious, my particle accelerator energy in GeV).

My problem is that I'm asked to now plot the transverse momentum

[tex]p_{T} = \lvert p_{f} \rvert \sin{\theta}[/tex]

I've been told that I am effectively trying to plot

[tex]\frac{\operatorname{d} \sigma}{\operatorname{d} p_{T}}[/tex]

and that I'll have to do some sort of histogram/binning to make my plot.

I'm not surewhatI should binning; the differentials, the final integrated cross section?

So, in essence, my questions is how can I plot [itex]\frac{\operatorname{d} \sigma}{\operatorname{d} p_{T}}[/itex] given that I have numerical data for [itex]\frac{\operatorname{d}\sigma}{\operatorname{d} \Omega}[/itex] (and [itex]\sigma[/itex])?

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# Homework Help: Computing a differential from plotted data

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