I have created plot of my model function:
energy[kx_,ky_]:=Sqrt[1-(Cos[kx/2]Cos[ky/2])^2]
using the material from question that I have previously asked (Energy band plotting), and I am getting plots like this:
Is there some way that I can add some data points (say some experimental measurements next to plotted model) in particular parts of given plot, say some data points from $(0,0)$ to $(\pi,-\pi)$, and some other data points in interval from $(\pi,0)$ to $(2\pi,0)$?

Show,Epilog? – Kuba Feb 11 '19 at 13:18Show/Epilogcarefully. If you're still stuck at this point, update this question to include the stuff you've tried, and explain why it doesn't do what you want. (As it stands now, your question is just a generic "how to put points on top of another plot" question, hence the closing as duplicate) – Lukas Lang Feb 12 '19 at 08:18