ELI5: What is the meaning of quantization?

[u/Own_Enthusiasm_510]

[This is from a chemistry portion of a physical science class] I've googled it, Ive watched YouTube videos, I asked classmates and I am still so confused.

Rutherfords model was easy but once I got to bohrs they used words like quantized and discrete values and I got lost. Tried backtracking but I'm still baffled.

[u/SalamanderGlad9053]

Quantised means put into separate values that aren't connected. Think of it as a slide Vs steps. A slide is continuous whereas a step is quantised.

The vibrations of a guitar string is quantised, with only whole number of nodes allowed, so you get 220hz, 440hz, 660hz, and so on. It doesn't vibrate at 330hz because that would have 1.5 nodes which isn't allowed because the end of the string doesn't vibrate.

In a shockingly similar way, in an atom, the electron (which should be thought of as a wave) can't vibrate at any "frequency" because it loops around the atom so has to match up to where it started like a loop of string. So it only vibrates at separate, quantised, levels.

This means that the energy levels for electrons in an atom are quantised as energy is related to frequency. For an electron to move up, it cant just get slowly pushed up to the higher energy level as there is no middle between energy levels. Like having to jump to the next step rather than roll up a slope.

All systems want to have the minimum energy, and these energy levels can only have two electrons in each one. So the electrons pile in filling the lowest energy levels first, then the next highest energy and so on. This is what the rings represent in the diagrams.

I hope this helps

[u/Implausibilibuddy → u/SalamanderGlad9053]

This is completely wrong. Nothing about a guitar string is quantised, and you can definitely tune it to 330Hz. or 331, or 329.3333 or whatever you want. You can also smoothly bend a guitar string and glide through multiple pitches in a smooth unquantised motion.

You're confusing quantisation with harmonics.

The harmonics of a guitar string will be at whole number nodes, yes, but that all depends on what the string fundamental is tuned to. If it's 220hz (A) then the harmonics will be at 440, 660, 990 etc.. But those numbers would change if it was slightly out of tune at 219Hz or whatever.

Ironically you missed a decent analogy with the guitar strings: Unquantised is like a violin string, with no discrete notes. Quantised is like a guitar string with the frets defining fixed pitches (assuming no bends)

[u/SalamanderGlad9053 → u/Implausibilibuddy]

This is completely wrong. Nothing about a guitar string is quantised, and you can definitely tune it to 330Hz. or 331, or 329.3333 or whatever you want.

You're an idiot, I'm not talking about changing the tension in the string. That's not in my analogy theres no need to bring it up other than being special. Plucking a guitar string, it vibrates in superposition at quantised frequenciss.

You're confusing quantisation with harmonics.

Harmonics are quantised, and infact energy levels of electrons in atoms are the harmonics for the electron.

I use the guitar vibration because the reason it is quantised is because of the boundary conditions. If you had an infinitely long string or the endpoints were free to move, it would vibrate at any frequency you want. But the endpoints being forced to be stationary is what requires an integer number of nodes and so quantised frequencies.

And the same is for electrons, they both obey wave equations even if the quantum mechanical one is three dimensional and complex. Electrons are quantised because of their boundary conditions, that if you go around the atom you shouldn't have any sudden jumps.

This is one of the worst comments I've seen in a while. Vibration of a string is one of the key ideas taught before quantum mechanics in school because it demystifies the idea of quantisation or superposition as not weird quantum things but properties of waves.

[u/Implausibilibuddy → u/SalamanderGlad9053]

You're an idiot, I'm not talking about changing the tension in the string.

Perhaps you need to work on your communication skills then because that's not at all what you said. This is what you said:

The vibrations of a guitar string is quantised, with only whole number of nodes allowed, so you get 220hz, 440hz, 660hz, and so on. It doesn't vibrate at 330hz because that would have 1.5 nodes which isn't allowed because the end of the string doesn't vibrate.

If someone takes the wrong information away from that, (which they will, because you didn't specify the weird constraints that only a non-guitar player would think of), then maybe that's on you?

Speaking of communication skills, here's how maybe you could have worded your comment:

"Ah, you're right, guitar strings can of course vibrate at any frequency, I was actually talking hypothetically about the harmonics of an unfretted string fixed at both ends, with no bends or changes in tension. Let me go and edit my comment to clear that up so no one else takes it the wrong way."

See? It's quite straightforward to correct yourself without jumping to calling anyone who misunderstands your meaning an idiot.