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The two main ideas that led to quantization are Planck's solution to black body radiation and Einstein's solution to the photoelectric effect. In both cases, we are dealing with absorption and emission by materials, which are comprised of several atoms.

If an electron jumps to a different state, we'll get a photon (or radiation) with energy $E=h\nu$. For materials, there will be many atoms, so we can say that a light stream is made out of photons of its corresponding frequency components.

But when it comes to accelerating a free electron, if we are able to move it back and forth somehow, we could either move it up and down at a low amplitude or at a high amplitude.

A high-amplitude wave would be said to be comprised of more photons than a low-amplitude wave. Eventually, we should be able to lower the amplitude to the point the energy of the wavefront is equal to that of a single photon. And technically we could go even lower.

This isn't possible with black bodies, photovoltaic cells and conductors because they use atoms for absorption and emission, and hence can only do so in discrete quantities, multiples of orbital jump energy requirements.

So is there any significance to the quantization of energy in contexts other than by atoms?

Kasiéobì ùdumágà
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Blacklight MG
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2 Answers2

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Eventually, we should be able to lower the amplitude to the point the energy of the wavefront is equal to that of a single photon. And technically we could go even lower.

There is a quantum version for the harmonic oscillator. The changes of amplitudes (energies) can be taken as continuous for the macroscopic world. Because they change in very small steps, $\Delta E = \hbar \omega$. But for small energies, the behaviour of the oscillator is very different from the classic version of the SHM, and the energy steps can not be ignored.

Claudio Saspinski
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  • But what is the theoretical proof for it? We chose that model to describe black body radiation and photoelectric effect, both for which there are intuitively discrete steps. The experiments show the results match, but is there any intuitive reason for us to prefer the existence of discrete steps in small scale SHM? – Blacklight MG Feb 10 '24 at 12:51
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    Quantum harmonic oscillator is a theoretical result of Schroedinger equation. But I agree that discrete steps are not intuitive. Perhaps the reason is: our everyday experience doesn't show anything like that. Without a spectrometer for example, the colour dispersion of light seems continuous. – Claudio Saspinski Feb 10 '24 at 12:59
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    @BlacklightMG Theoretical proof? That's not physics. The phenomena rule. – John Doty Feb 10 '24 at 13:29
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To convince yourself that photons really exist as quantum particles, take a look at en.m.wikipedia.org/wiki/… (en.m.wikipedia.org/wiki/Double-slit_experiment). The gif shoes how discrete quanta of energy reach the screen even though the light source may have continuous energy levels.

Note that the question whether light consists of discrete quanta is distinct from the existence of discrete versus continuous energy levels. These two distinct phenomena are mixed up in your question "So is there any significance to the quantization of energy in contexts other than by atoms?"

my2cts
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    "Note that the question whether light consists of discrete quanta is distinct from the existence of discrete versus continuous energy levels. These two distinct phenomena are mixed up in your question" - thanks that was helpful. As for the double slit experiment, I was confused whether the photons were really absorbed or if it was that the center spot of collision was relatively more bright compared to the surroundings, making it seem like a single dot. Turns out single photon avalanche detector arrays show that a current is only generated in one of the detectors in the grid per photon. – Blacklight MG Feb 14 '24 at 08:55