Is quantization a consequence of the wave nature of particles? Elucidate.
I think a good approach to answering your question, is to make a timeline of quantization, then things get more clear for you.
(Don't know the year): Boltzmann considers quantized energy levels for deriving his distribution.
1900: Planck proposed a frequency distribution for black body radiation in agreement with experimental data. He then showed that if the energy content of the oscillators in the black body is assumed to be quantized, his distribution will follow.
1905: Einstein applied the notion of light quanta to the problem of photoelectric effect leading to a satisfactory explanation which proved such a notion to be close to reality.
1913: Bohr proposed his atomic model inspired by Einstein's and Placnk's ideas.
1915: Sommerfeld (and maybe others too) generalized Bohr's model and proposed a mathematical quantization rule.
There is of course much more than that to the history of quantum theory but these are the starting points of quantization. So it was started as a good postulate that could produce results in agreement with experiment.
But then Heisenberg and Schrodinger proposed their theories.
I think Heisenberg also postulated quantization rather than deriving it, I'm not sure. But Schrodinger did derive quantization from his wave mechanics. Quantization is mainly because of the restrictions made by boundary conditions. That's how it arises mathematically. I don't know if there is an explanation in terms of physical principals.
But other formulations of QM also give rise to quantization so I can't say yes as your answer.
I think we always talk about the wave nature of particles because wave mechanics is the most popular formulation of QM otherwise other formulations don't suggest such an interpretation, at least not explicitly.
So I can only say that Quantization is a consequence of Quantum Mechanics.
Its a consequence of the principles of QM that were fully developed in 1927 when Dirac came up with his transformation theory in 1927 which is what is generally known as QM today.
The so called wave particle duality is basically a crock of the proverbial that was consigned to the dustbin by Dirac's theory.
Also things in QM are not necessarily quantised - eg a free particle.
If you want to see the true basis of QM check out:
For a more axiomatic view see post 137:
But why does it really matter in the larger scheme of Particle Physics?
Actually, I would be inclined to say that "quantization" is the result of the particle nature of waves!
As all good physics quantum theory is the result of careful observations and experiments in the real world. Physics is an empirical science with strong help from mathematical theories that summarize the observations in (an astonishingly small number) of fundamental Laws of Nature.
It is as wrong to say particles have wave properties or waves (fields) have particle properties. The only true picture is simply provided by modern quantum theory. That's it, not more, not less. Oldfashioned pictures from the 25 years between the discovery of the quantum nature of the interaction of electromagnetic fields with matter by Planck (black-body radiation) and the discovery of modern quantum theory by Heisenberg, Born, Jordan, Schrödinger, and Dirac & Co. should be abandoned from the classroom and the scientific and popular science literature, with the only (important) exception of studies about the history of (quantum) physics.
That's closer to the truth which lies not in QM but QFT - but of course still not really true.
What picture would you present to a 10th grade high school student?
The following book:
Dirt cheap as a Kindle version.
And it has the virtue of being TRUE.
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