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

  1. Apr 29, 2010 #1
    i'm new here and i'm not sure if this has been asked before, but i'm just wondering about the cause of its existence. i'm speculating that it may be caused by interaction between a proton and electron together with their masses, if so, how?
  2. jcsd
  3. Apr 29, 2010 #2
    I'm going to help you out a bit here and say that most likely you're not going to get an answer as it's not a question. I'll use a phrase I do actually use with my wife when she asks me things that are not questions. it's like asking
    "Why does July taste like the color purple?"
    It's not said to be rude or mean but to bring humor in asking a non-question.

    your question contains asking why things are the size they are, is that your question?
  4. Apr 29, 2010 #3
    Boundary conditions..

    The blackbody radiation experiment had boundary conditions.

    QM equations have boundary conditions, even if we have to make the length between boundaries go to infinity.

    Let's remove boundaries then.

    Take the free particle hamiltonian energy eignvalue equation. The energy eigenvalues are p^2/2m where p is continuous. No more quantum levels.
    Last edited: Apr 29, 2010
  5. Apr 29, 2010 #4
    Okay but that's not the cause for that scale, it's the equations to work in those scales. And unless I misunderstand your hamiltonian Eq, your setting the energy level of the plane wave high enough so that the eigenvalues becomes close enough to be free particles?, that really doesn't do away with the quantum level but removes that upper boundry. do correct me if I'm off on that.

    To me the question from the OP is the equivalent of asking what is the cause for finer resolution? which really isn't a question at all.
  6. Apr 29, 2010 #5
    i don't think it is a non-question at all, i may just be referring to reality as to what might be a physical or at least a theory that may explain its physical cause, but just to make my self clearer, i will rephrase my question: what i'm asking is what causes the existence of the the thing that keeps electrons in place?
  7. Apr 30, 2010 #6
    The Uncertainty Principle. As the electron becomes more isolated in space (closer to the nucleus) the electron's probability for a higher and higher momentum increases. This is another example of the wave like properties of an electron, uncertainty has always been a factor in even classical wave mechanics.

    The boundary conditions of the central potential determine exactly what the lowest state can be.

    Funny how uncertainty gives us certainty in so many things, in the end its uncertainly certain.
  8. Apr 30, 2010 #7
    stop miss using the uncertainty principle! it has to do with observations not energy levels

    Have you done your QM class boy??...
  9. Apr 30, 2010 #8

    http://www.physics.sfsu.edu/~greensit/book.pdf [Broken]

    Page 90 "Why the hydrogen atom is stable"
    Last edited by a moderator: May 4, 2017
  10. Apr 30, 2010 #9


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    You might want to watch your tone ... especially since you are wrong. The HUP has to do with whether or not observable quantities can be simultaneously well-defined ... it is completely independent of measurement or observation. The HUP sets a lower limit on the width of distributions from which non-commuting observables are sampled, so it is often explained in terms of observed distributions for repeated measurements. However it is far more fundamental than that, and actually is directly derivable from the postulate that quantum states are representable as vectors in a Hilbert space.
  11. Apr 30, 2010 #10
    those derivations are just heuristic pseudo arguments found in introductory books
    Last edited by a moderator: May 4, 2017
  12. Apr 30, 2010 #11
    are you cute?

    I said that HUP has to do with measurements and not energy levels, I had no time to give a full derivation of HUP
  13. Apr 30, 2010 #12
    Enlighten us ansgar.
  14. Apr 30, 2010 #13
    Yes, but if you questioned them seriously, you would be aware that those derivations can be carried over quite far in full QFT, and although they must certainly be taken with a grain of salt, still they remain quite suggestive.

    In "The quantum vacuum, introduction to QED" Milonni discusses in section 2.6 how the momentum-position commutator for a charged particle would be damped exponentially to zero without fluctuations of the electromagnetic field to which it couples. That is because we can couple a charged particle to its own field.
    Then in section 3.3 he goes on to atomic stability. He applies the same ideas, balancing how much the electron absorbs energy from the vacuum to how much it gives away, and obtains... Bohr quantization condition
  15. Apr 30, 2010 #14
    "Uncertainty" is quite a badly chosen name. The inequality is nothing but the Cauchy-Schwarz inequality. This is so well-known, it is in the introduction of a wikipedia article. Seriously, this is elementary Hilbert space theory.
  16. Apr 30, 2010 #15
    It is because of this inequality and functions having the properties of vectors that we have uncertainties right?
  17. Apr 30, 2010 #16
    There is no "uncertainty" per se in the inequality, since there are some people advocating non-local hidden variable theories who will interpret that all variables are always well-defined, and they have not convincingly been proven wrong.

    Second, there is no "principle" per se in the inequality either, as explained for instance here
    Otherwise, yes, the inequality is best understood geometrically, thinking of functions as vectors.
  18. Apr 30, 2010 #17
    I have heard mixed opinions about hidden variables. It is beyond my current knowledge as I am not even taking QFT or QED yet, just core. Some interesting stuff you posted though.
  19. Apr 30, 2010 #18
    Please note that I am not lobbying for any interpretation. I only point out that Heisenberg's inequality does not mathematically imply fundamental uncertainty.
  20. Apr 30, 2010 #19
    so you don't know how to derive it but still uses it as if you know what it is?

    there are library items here on the forum which is really good, have a look at them.
  21. Apr 30, 2010 #20


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    Yes, and I said that you were wrong, and pointed out why I think so. Do you have a rebuttal?
  22. Apr 30, 2010 #21
    I can derive the existence of discrete energy levels without the HUP if that is what you mean by rebuttal?
  23. Apr 30, 2010 #22
    I thought we were using HUP to prove how atoms can be stable. The OP question changed after a couple posts.

    I was saying that boundary conditions are the reason for discrete energy levels.
  24. Apr 30, 2010 #23
    HUP is an integral (maybe the most fundamental) part of quantum theory, so much so that without it Quantum Mechanics becomes "Classical Mechanics"... And needless to say, you don't have any discrete levels in classical mechanics. So, no, without HUP you cannot "derive" anything..
    (Solving a wave equation in 1D with the simplest boundary condition does not qualify for a theory, if that's your secret derivation!..)
  25. May 1, 2010 #24
    Atoms are stable without hup
  26. May 1, 2010 #25
    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?
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