# I'm just wondering, what causes the existence of quantum levels?

yes it as an important thing, but people are miss using it since they don't really know where it comes from, can YOU derive it?

you do have quantization in CM, nodes in a flute, string or whatever!

you don't need and should not use HUP to derive energy levels in an atom and why it is stable! HUP is the standard deviation of measurment of momentum times the standard deviation of position is greater than hbar/2.

all we can say about the hydrogen atom is about standard deviations of it's energy levels etc, NOT absolute values!

Do you want me to call ZapperZ to step in here and judge who of you and I are correct?
Without HUP, your electrons become purely classical, "guitar" frequencies, and your theory falls apart very quickly.. I think this is rather obvious, in fact in many contexts $\hbar \rightarrow 0$ limit is invoked to re-derive classical formulas from QM. [ And that's what you are doing by completely disregarding HUP.]

"Just" stealing Schrodinger equation from QM, and doing a few calculations fails pretty quickly.. It's simply not QM anymore, without HUP..

Of course ansgar is correct that one does not explicitly need HUP to "derive" the stability of atoms. But if one wants to adopt this line of thought, one doesn't actually need HUP for anything, since it's fully included in the quantum theory itself. But HUP is still such an important relation, since it compresses a big part of quantum "weirdness" into a small and simple relation. Therefore, HUP is almost always an excellent starting point when one wants to understand the simplest effects of quantum mechanics heuristically. So in my opinion, if one wants to take a first step into understanding QM by considering HUP, there is nothing wrong with that.

Feynman once said something about how important it is to know many ways to derive one result.

Of course ansgar is correct that one does not explicitly need HUP to "derive" the stability of atoms. But if one wants to adopt this line of thought, one doesn't actually need HUP for anything, since it's fully included in the quantum theory itself. But HUP is still such an important relation, since it compresses a big part of quantum "weirdness" into a small and simple relation. Therefore, HUP is almost always an excellent starting point when one wants to understand the simplest effects of quantum mechanics heuristically. So in my opinion, if one wants to take a first step into understanding QM by considering HUP, there is nothing wrong with that.

Feynman once said something about how important it is to know many ways to derive one result.
yes of course HUP can be used to MOTIVATE certain (all) results in QM, but HUP is not special to QM either - it exists in signal analysis etc. as well! Thus the key concept to all QM "understanding" lies in what postulates - i.e. which interpretation of QM - one adopts.

The reason for why the energy levels are discrete in atoms are due to properties of the wave equation and that one assigns energy to those eigenfunctions. For other waves we don't think that discretezation is funny or weird, like standing waves on a drum for instance. All the phenomenon in QM exists in classical mechanics, but the interpretation is different.

Without HUP, your electrons become purely classical, "guitar" frequencies, and your theory falls apart very quickly.. I think this is rather obvious, in fact in many contexts $\hbar \rightarrow 0$ limit is invoked to re-derive classical formulas from QM. [ And that's what you are doing by completely disregarding HUP.]

"Just" stealing Schrodinger equation from QM, and doing a few calculations fails pretty quickly.. It's simply not QM anymore, without HUP..
HUP exists classically as well.

so now I have one more guy supporting me that HUP is "heuristically" i.e. not really fundamental...

I am a teacher at university in QM classes, who are you?

HUP exists classically as well.
There definitely are analogues of HUP in classical physics as well, but we are talking about point particle mechanics here. And in classical point particle mechanics, there is no HUP. So when one applies HUP to a point particle, one is doing QM, and it is this HUP that everyone is talking about here.

There definitely are analogues of HUP in classical physics as well, but we are talking about point particle mechanics here. And in classical point particle mechanics, there is no HUP. So when one applies HUP to a point particle, one is doing QM, and it is this HUP that everyone is talking about here.
HUP for waves in classical mechanics exists.

QM is sort of a mixture of point particle classical mechanics and waves, hence the old name "wave mechanics"

SpectraCat
HUP exists classically as well.

so now I have one more guy supporting me that HUP is "heuristically" i.e. not really fundamental...

I am a teacher at university in QM classes, who are you?
No, he only said that the HUP is not unique ... he seems to me to be arguing that it is fundamental to Q.M. ... read that last line of his post again:

It's simply not QM anymore, without HUP".
In my experience it is much easier to get students to understand and anticipate many quantum phenomenon starting from the HUP. Take zero point energy for instance ... early in my class I was able to get my students to predict the existence of zero point energy, just by asking them to think about what must happen in terms of the HUP when a particle is confined in a particular region of space. Similarly, I used the HUP to explain why, for a given system, the energy of an eigenstate increases with the number of nodes in the wavefunction. Another great example is the triple Stern-Gerlach experiment, which is another great illustration of the fundamental nature of the HUP, and how some of it's ramifications were directly evident in very clear ways in the early experiments that established the foundations of QM.

I have found that this kind of qualitative understanding really helps the students to keep up with the course material, and to keep it as part of their general knowledge when they leave the course.

HUP exists classically as well.

so now I have one more guy supporting me that HUP is "heuristically" i.e. not really fundamental...

I am a teacher at university in QM classes, who are you?

I am a graduate student so you think that makes your point stronger?
I think this is a pointless debate. I think it's not my duty to "convince" you that HUP is fundamental to QM and without it, all the interesting quantum phenomena wouldn't exist.

I honestly don't know what you are arguing against here besides, well, this one's almost verbatim from Feynman, so who are you?

Ad hominem arguments won't resolve anything.

I am a graduate student so you think that makes your point stronger?
I think this is a pointless debate. I think it's not my duty to "convince" you that HUP is fundamental to QM and without it, all the interesting quantum phenomena wouldn't exist.

I honestly don't know what you are arguing against here besides, well, this one's almost verbatim from Feynman, so who are you?

I would say that HUP is fundamental but not the ONLY and MOST fundamental thing. The MOST fundamental thing is the wave function which is used to DERIVE HUP, i.e. HUP is not more fundamental than the schrödinger wave equation for instance (which is used to derive energy levels in eg. the hydrogen atom). So that was a good argument from my side, HUP is not the most fundamental thing and that interesting phenomena do exists without using it.

HUP gives the standard deviation time standard deviation in position > hbar/2 i.e an upper limit - is that really so hard to accept? Now since it gives the limit of things, it can be used heuristically to give a FEELING and orders of magnitude estimates. It is not strange that HUP gives "ok" results, it only shows that QM is self consistent.

So i stress again, the most fundamental thing is the wave function - without it - no interesting phenomena would exist ;)

alxm
Seems you're just disagreeing on what 'fundamental' means.

The HUP is 'fundamental' in the sense that it's a basic, and very general result of QM.
But it's not 'fundamental' in the sense of being a fundamental postulate QM is built on.
You have to have QM to derive the result.

Sure, it makes for a nice heuristic which can be used to explain why atoms are stable, but you're just explaining one QM result in terms of another then.
Similarly, you could explain the atom in terms of the 1d particle-in-a-box, showing that the energy levels increase as the size decreases,
and thus it's this 'confinement energy' which balances the nuclear attraction. (and as an added bonus, you also explain the Rydberg formula)

The argument seems to have changed into a discussion of uncertainty, but as to the OP, the electron is held in the atom by potential energy differences. If you accept that electrons have De Broglie wavelengths, they can only exist around the electron at specific radii, otherwise they would destructively interfere with themselves and stop existing, which causes the discrete levels observed. This is, of course, somewhat of a simplification, but the concept is there.

The argument seems to have changed into a discussion of uncertainty, but as to the OP, the electron is held in the atom by potential energy differences. If you accept that electrons have De Broglie wavelengths, they can only exist around the electron at specific radii, otherwise they would destructively interfere with themselves and stop existing, which causes the discrete levels observed. This is, of course, somewhat of a simplification, but the concept is there.
Then what is the mediator between the electron's wave function and the electron itself that tells the electron to stay put?

The electron is indistinguishable from its wave function. Electrons are not strictly particles or waves, but exhibit characteristics of both. The wave function is just a convenient representation of the square root of the probability of the electron being observed in a given location.

The electron is indistinguishable from its wave function. Electrons are not strictly particles or waves, but exhibit characteristics of both. The wave function is just a convenient representation of the square root of the probability of the electron being observed in a given location.
So we know why the electron is held in place and does not crash into the nucleus though we don't know how. There is no observable holding it in place.