I am confused, hydrogen just has one electron in the 1s orbit. but why can we plot all kind of orbitals (higher energy eigenstates for that atom)? My assumption: So physically spoken these orbits around the hydrogen nucleus exist and they go to infinity, but they are just empty?
Additional question: When we want to plot orbitals of other atoms e.g. silicon, we need to use numerical methods. So instead of doing complex numerical methods, do we use simply the hydrogen solutions as approximation then?
Is there a big difference between let's say the shape of a numerically solved silicon p-orbital and an analytically solved hydrogen p-orbital?