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What reasons does de Broglie had when he proposed the idea that electrons behave like waves?

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  • $\begingroup$ One of the sources of this guess was that electromagnetic radiation already displayed both wavelike (interference) and particle-like (photoelectric/Compton effect) properties. The guess was that this could be extended to other particles. $\endgroup$
    – Avantgarde
    Commented Oct 3, 2018 at 7:53
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    $\begingroup$ I can't help feeling this is a question about history rather than physics, and it would be better on the History of Science Stack Exchange. $\endgroup$ Commented Oct 3, 2018 at 8:01
  • $\begingroup$ @Avantgarde, yes but there is a fundamental difference between light (photons) and matter (eg. electrons). My question is: why should (we think that) matter also display this dual behaviour? Usually the idea that you are left with is: why not? Let's see if that is ideed the case... And it was, it was verified experimentally. But it seems that it was not even an educated guess. It happened to be that way. $\endgroup$ Commented Oct 3, 2018 at 8:37
  • $\begingroup$ @JohnRennie, Yes, I also think that this question could have been posted to History of Science and Mathematics as well. This question is about (at least this is my intention) how a physicist thinks, how breakthroughs in physics are being made, but it could also reveal a deeper understanding that perhaps I and others do not have about quantum mechanics. $\endgroup$ Commented Oct 3, 2018 at 8:49
  • $\begingroup$ @AWanderingMind It was a good guess, but that's all that matters. There are all kinds of particles in nature. If you observe some general property (wave-particle duality) in one of particles (photons), you can't help but think of this property as a unifying aspect in all other particles. I suppose this idea of 'unification' of different particles under one property was motivating. $\endgroup$
    – Avantgarde
    Commented Oct 3, 2018 at 9:48

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The answer to this question can be found in de Broglie's Nobel Lecture. The pdf file is available here. I quote the relevant part.

The necessity of assuming for light two contradictory theories -that of waves and that of corpuscles- and the inability to understand why, among the infinity of motions which an electron ought to be able to have in the atom according to classical concepts, only certain ones were possible: such were the enigmas confronting physicists at the time I resumed my studies of theoretical physics.

When I started to ponder these difficulties two things struck me in the main. Firstly the light-quantum theory cannot be regarded as satisfactory since it defines the energy of a light corpuscle by the relation $W=h\nu$ which contains a frequency $\nu$. Now a purely corpuscular theory does not contain any element permitting the definition of a frequency. This reason alone renders it necessary in the case of light to introduce simultaneously the corpuscle concept and the concept of periodicity.

On the other hand the determination of the stable motions of the electrons in the atom involves whole numbers, and so far the only phenomena in which whole numbers were involved in physics were those of interference and of eigenvibrations. That suggested the idea to me that electrons themselves could not be represented as simple corpuscles either, but that a periodicity had also to be assigned to them too.

I thus arrived at the following overall concept which guided my studies: for both matter and radiations, light in particular, it is necessary to introduce the corpuscle concept and the wave concept at the same time. In other words the existence of corpuscles accompanied by waves has to be assumed in all cases. However, since corpuscles and waves cannot be independent because, according to Bohr’s expression, they constitute two complementary forces of reality, it must be possible to establish a certain parallelism between the motion of a corpuscle and the propagation of the associated wave. The first objective to achieve had, therefore, to be to establish this correspondence.

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  • $\begingroup$ Ok, so that fact that electrons can only be in some particular "quantized orbits", lead de Broglie to think that they must also exibit some wave-like behaviour. $\endgroup$ Commented Oct 3, 2018 at 11:12
  • $\begingroup$ Yes, I think so. In addition to that I think he was encouraged by the "fact" that light was already behaving in this (wave-particle) way. $\endgroup$ Commented Oct 3, 2018 at 11:18

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