For a summer class, I’ve been trying to get the quantum picture of an atom at least in conceptual terms, no math. I understand how, if you think about an atom like a one-dimensional box, an s orbital is like the first fundamental wave, and a p-orbital is like a sine wave, and I understand how the p orbital has higher energy because of greater frequency. But how can you picture 2s and 3s, etc. orbitals? Are they like first fundamental waves with greater amplitudes? I thought that the frequency of a fixed string depends mainly on its length and tension, not amplitude, so if that's the case how does E = hv? Also, how are they quantized, since can’t you “pluck” that string in a one-dimensional box however far you want (at least as far as it can stretch), and give it an infinite number of amplitudes? In other words, I get how the need to fit a whole number of half wavelengths into the box justifies the quantization of energy into s, p, d, etc orbitals, but what limitation prevents the s orbitals from having a continuous spread in energy?