I have a function depending r, for example
f[r_]:=2*(1/a)Exp[-r/a]
I want to plot a r^2 f[r]^2 vs r/a, How to do this? I tried this
Plot[a *r^2 *f[r]^2, {r/a, 0, 8}, PlotRange -> All] but it returns $Failed
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1 Answer
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Plot isn't designed to handle arbitrary expressions as a domain. Replace r with a rdividedbya where rdividedbya is a symbol name that the language can use.
Plot[a*r^2*f[r]^2/.r->a rdividedbya,{rdividedbya,0,8},PlotRange->All]
This replacement happens before the expression a*r^2*f[r] is evaluated and is effectively the same as
Plot[a*(a rdividedbya)^2*f[a rdividedbya]^2,{rdividedbya,0,8},PlotRange->All]
Replacement saved us the work of typing a rdividedbya twice. We could even be so lazy as to solve the equation $\text{rdividedbya}=\frac ra$ for $r$ with Mathematica, but that's overkill in this situation.
