Do equidistant energy levels necessitate a harmonic potential?

Abstract Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only yields finite range and with nonzero uncertainty. Within study we review isospectral potentials the investigate applicability of hypothesis to recent measurements. First, describe experimental model, obtaining realistic size depth resulting quantum well. Second, use shift-operator approach calculate anharmonic non-polynomial producing (partly) spectra. We discuss different potential types interpret possible modeling applications. Finally, applying n th order perturbation theory exactly  eigenenergies cannot be achieved polynomial potentials, except potential. In summary, aim give an overview over which conclusions may drawn determination not.