I think the data in figure 2 of this paper does a great job of showing the decrease in spacing in energy as the quantum number increases, as well as the change in energy of a particular state with well thickness:
"Quantum well states and short period oscillations of the density of states at the Fermi level in Cu films grown on fcc Co(100) " P. Segovia, E.G. Michel, J.E. Ortega Physical Review Letters 77 (16) (1996) 3455-3458<tel:(1996)%203455-3458>.
For many years it has bugged me that we never show students any experimental data to compare to the calculated energy levels of a one-dimensional infinite square well. Does anyone know of such data? Obviously the 1-D infinite well involves many idealizations that will hold only approximately for actual physical systems, natural or fabricated. But the essential result, it seems to me, is a quantum ladder of energy levels that get farther apart as you go up. Can anyone point me to an experimental energy level diagram that has this property?
Dan Schroeder
Physics Department
Weber State University