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It is said that de Broglie explained the quantization of Bohr's orbitals with the idea of the "matter wave" of the electron being forced to have orbits where it can interfere constructively with itself as a standing wave on a circle.

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My question is: what is the reason why the non-constructive orbits would be "forbidden"? Why can't we accept a situation where the wave can travel on the orbit with irregular superpositions or maybe totally destructive interference of the wave?

(Illustration from here)

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The Bohr model is tied with quantization of angular momentum by demanding standing waves for the orbit.

There would be no quantization if the wave is not standing. The model is successful in reproducing the spectral series of the Hydrogen atom. That was its success, that the observed quantization of energy could be derived from this assumption, as seen in the link. It is not a matter of "accepting" but of solving with this hypothesis for energy levels and agreeing with data.

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  • $\begingroup$ As far as I know Bohr's model (1918) was still not considering waves for the electrons, Bohr just quantized the angolar momentum. It was the Broglie that later (1925) suggested the idea that the quantization could be explained with his "matter wave" hypothesis, I am asking why this would actually explain the quantization. $\endgroup$ May 22, 2021 at 12:12
  • $\begingroup$ The link has the mathematics. Maybe the "wave picture" came later, but once one models a wave, the mathematics inevitably gives standing waves. $\endgroup$
    – anna v
    May 22, 2021 at 12:36
  • $\begingroup$ Ok but standing waves don't exist only in normal modes $\endgroup$ May 22, 2021 at 12:46

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