I have read the description of electrons as standing waves based on an analogy with a string vibrating at its natural frequencies: thus the different quantum levels are akin to the tones or harmonics of the string, right? So far, so good, but then I have seen contradictory complementary views: - One is that Planck introduced an "additional restriction or condition": that the energy levels where the electron oscilates are quantized. - Other explanations instead do not talk about such additional thing, they just use the above mentioned analogy without seeking a differentiation with the macroscopic case. I tend to think that the second interpretation is the right one. After all, the basic idea is that, to excite the electron to a higher level, one needs a photon, for example, of the right frequency. Then it can be the fundamental one (f) or the same multiplied by an integer (nf). So one could say that the interaction frequencies are quantized. And then one can convert frequency into energy by multiplying it by the Planck constant, which acts as a conversion factor (E = h n f). Conclusion: one could equally say that to create a standing wave in a string you need the appropriate quantums of energy or that to create a standing wave in an an atom you need to play it with notes of its harmonic series... Is this right?