In the lecture notes in the LCAO Model notes, there’s a figure towards the end where you have drawn \psi_- and \psi_+ and you state that according to the node theorem, wavefunctions with lower energies have fewer points where the wavefunction is zero. However, I do not see this as the case in the plot that’s given there. It says that between the two atoms \psi_- is 0 and \psi_+ is not. But I do not see this in the plot? The \psi_- just has one of its peaks mirrored. Can you explain what that plot is showing and how I can see what’s described in the notes in it?
From the plot this is not so clear. However, note that \psi_+ is the symmetric superposition of two orbitals and \psi_- the anti-symmetric one. Try adding e.g. two Gaussians and check if you get zero in the middle. Then flip one of them and add them again.