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Using de Broglie wavelength we can explain the concept of how the electrons moved around in fixed circular orbits by saying those are the standing waves in which the electron moves around the nucleus in resonant conditions.

However, from my understanding, it is still a concept that is used in modern quantum mechanics. So, in what way does the way the postulate is used to explain phenomena in modern quantum differ from how it was used to explain the Bohr atom?

I'm particularly interested in how the application of the de Broglie postulated as an explanation of the circular orbits in which the electrons move was found to be wrong.


Reference:

This answer was inspired by this answer on PSE

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The de Broglie hypothesis of matter waves is incompatible with the experimental results, for example, the double slit single electron at a time, where the footprint of the electron is compatible with the point particle axiomatic definition in the standard model of physics, it is not spread out in space. The wave nature appears in the accumulation of electrons.

The Bohr model was good enough before the development of the theory of quantum mechanics with its postulates but was superseded by the solution of the qm wave equations, which gave a lot more verifiable by experiment predictions atomic behavior. There the Bohr orbits become the orbitals, probability loci.

But physics models can still be useful in specific problems, simplifying more complex situations conceptually, so the Bohr model may be still used for rough approximations and the de Broglie wavelength for order of magnitude estimates compatible with both the quantum mechanical and the qualitative hypothesis of matter waves.

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  • $\begingroup$ In the post one of the comment is written: " The de Broglie rule for wave-lengths lives on, but it's application is either in BoTE techniques or buried in the details of full blown quantum pictures (it is most visible in the wave mechanics). –" This suggests that at least the wavelength part of the matter wave is still used. Now, how is exactly is this part used? $\endgroup$ Nov 7, 2020 at 15:06
  • $\begingroup$ I thik it is just as a useful tool as I say in my answer., one could interpret the orbital loci as "matterwaves" I suppose, keeping in mind the probability of detecting the matter/pont-particle. $\endgroup$
    – anna v
    Nov 7, 2020 at 16:01
  • $\begingroup$ The point I am stuck on is how they are used useful tools? Initially it was thought that they gave resonant wavelengths for which electron orbits but that is wrong, so how was it reinterpreted? However, you have correctly addressed the point in the second part of my question i.e: how it was found to be wrong $\endgroup$ Nov 15, 2020 at 8:10
  • $\begingroup$ maybe the answers to this question will help?google.com/… $\endgroup$
    – anna v
    Nov 15, 2020 at 8:40
  • $\begingroup$ I do have some concept of the Schrodinger model and the Bohr model, however, I just can't understand how a wrong concept in one theory is used again in another theory correctly. Some say that in modern QM it gives the measures at which quantum is applicable, but I'm not sure how that works exactly $\endgroup$ Nov 15, 2020 at 9:57

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