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Does quantum mechanical definition of momentum require movement ?

  1. Apr 18, 2009 #1
    Does quantum mechanical definition of momentum require "movement"?

    If quantum mechanical definition of momentum does not require "movement", then why "white dwarf star" won't collapse? How can it resist the pressure of gravity in the star?
    http://en.wikipedia.org/wiki/White_dwarf

     
  2. jcsd
  3. Apr 18, 2009 #2
    Re: Does quantum mechanical definition of momentum require "movement"?

    I'm not sure what this has to do with "movement" really, but white dwarfs stars only don't collapse if they are held up by the appropriate http://en.wikipedia.org/wiki/Electron_degeneracy_pressure" [Broken] for full details though, because White Dwarfs can collapse/supernovae.
     
    Last edited by a moderator: May 4, 2017
  4. Apr 18, 2009 #3
    Re: Does quantum mechanical definition of momentum require "movement"?

    But how can it resist the pressure of gravity if no "movement" is involved?
    For example, the reason balloons won't collapse is that the gas molecules inside it are moving, so the momentum resist the pressure in it
     
    Last edited by a moderator: May 4, 2017
  5. Apr 18, 2009 #4
    Re: Does quantum mechanical definition of momentum require "movement"?

    Read what I just wrote about electron degeneracy pressure.
     
  6. Apr 18, 2009 #5
    Re: Does quantum mechanical definition of momentum require "movement"?

    I already knew electron degeneracy pressure.
    The question is the electron degeneracy pressure involve the "movement" of electrons or not.
     
  7. Apr 18, 2009 #6
    Re: Does quantum mechanical definition of momentum require "movement"?

    Then what is your question? Why are you assuming that movement is needed? What kind of movement are you thinking about?
     
  8. Apr 18, 2009 #7
    Re: Does quantum mechanical definition of momentum require "movement"?

    Like the "movement" of the gas molecules inside the balloon
     
  9. Apr 18, 2009 #8
    Re: Does quantum mechanical definition of momentum require "movement"?

    Yes, but that's not the kind of pressure that is holding a white dwarf up. The matter is too close together to be moving like that, the thing that is keeping it apart is the Pauli Exclusion principle. No motion needed, or possible, really.
     
  10. Apr 18, 2009 #9
    Re: Does quantum mechanical definition of momentum require "movement"?

    The calculation of <degenerate matter> does involve "movement" or speed of the electrons.
    See this link:
    http://books.google.com/books?id=P_...Goa&sig=ZkzEIBINItUiFyMW5-uvjt1kMus#PPA143,M1
     
  11. Apr 19, 2009 #10

    alxm

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    Re: Does quantum mechanical definition of momentum require "movement"?

    Says who? Quantum mechanical particles most certainly do move. While they do not have the same properties as a classical particle, as in an exactly defined position or momentum, that doesn't mean they do not move.

    Quantum mechanical particles have momentum, they have kinetic energy, they display all the dynamical effects of motion. It's simply wrong to think that, for instance, a particle in a bound state doesn't move. It's analogous to saying that a classical standing wave isn't moving.
     
  12. Apr 19, 2009 #11
    Re: Does quantum mechanical definition of momentum require "movement"?

    Quantum mechanical objects have no rest, thez are always in "motion". Think to the quantum harmonic oscillator which has no zero energy mode.
     
  13. Apr 19, 2009 #12
    Re: Does quantum mechanical definition of momentum require "movement"?

    See this link, https://www.physicsforums.com/showthread.php?t=304954
     
  14. Apr 19, 2009 #13
    Re: Does quantum mechanical definition of momentum require "movement"?

    I think that the term 'movement' is unnecessary and vague when talking about phenomena that are dominated by quantum effects. In this regime the wave nature of matter is important, and so it is not clear what is moving (it's not a particle, it's not a fluid) so it just makes more sense to give a description in terms of waves (scalar fields) that are a function of space and time.
     
  15. Apr 20, 2009 #14
    Re: Does quantum mechanical definition of momentum require "movement"?

    I completely agree with you.
     
  16. Apr 20, 2009 #15

    alxm

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    Re: Does quantum mechanical definition of momentum require "movement"?

    What 'makes sense' depends entirely on the context. Referring you to the recent post on Hartree-Fock, I'd challenge you to give a rationalization of electronic (Coulomb) correlation that doesn't rely on using the idea of 'motion'. Moreover, electrons do not self-interact; which they would if they were simple semi-classical 'density fields'.

    I said it before but I'll say it again: Neither the 'particle' or 'wave' description is correct. And if you tell people that 'quantum particles don't move', then you're setting them up for other misunderstandings farther down the road.
     
  17. Apr 20, 2009 #16

    f95toli

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    Re: Does quantum mechanical definition of momentum require "movement"?

    I think we are arguing about semantics here. The reason why I don't think one should talk about "motion" in this case is that people will inevitably think of the classical concept. One advantage with the concepts such as momentum, kinetic energy etc is that they are quite abstract (and more "mathematical) even in classical physics, meaning there is less risk of misunderstanding about what they mean in QM. There is-as far as I know- no obvious reason why one would need to keep the link between motion and momentum/kinetic energy that exists in classical physics when we move to QM.

    The point is that we must -in my view- always remember than ANY form of "visualization" of concepts in QM (and physics in general) can never be more than tools to help us understand what is going on (i.e. predict the outcome of experiments) and I think one should emphasise this when teaching QM; there is no reason to believe that the pictures we draw have anything to do with an underlying reality (whatever that means).
     
  18. Apr 20, 2009 #17
    Re: Does quantum mechanical definition of momentum require "movement"?

    I think it's wrong to say that quantum particles do not move. For example, the double-slit experiment, The electrons must "move" from the source and pass through both slits, then reach the screen, in order to generate interference pattern. However we do not know the exact path it takes. So we do not know how electrons move from point A to point B if they are not observed, but that does not mean electrons do not "move" in space, otherwise, how can the interference pattern show up?
     
    Last edited: Apr 20, 2009
  19. Apr 20, 2009 #18
    Re: Does quantum mechanical definition of momentum require "movement"?

    The same story again...Hootenanny's that post is a little misleading as stated by himself later in that post.

    Concept of movement not only makes perfect sense in the quantum sense, but also is absolutely ESSENTIAL in understanding QUANTUM TRANSPORT.

    Guys, please, I am doing my Ph.D on quantum transport, where there's ALWAYS movement. The whole field is built on dynamics, movement, current flow operators etc... The computer you are using right now is governed by MOVING electrons.

    The fact of the matter is, whether you treat it classically or quantum mechanically, gate capacitors of the transistors in your laptop is being charged right now by MOVING electrons.

    Doesn't matter your abstract Hilbert space formulation shows it or not.

    This is the reality.

    For more info:
    See my post in that link above.


    And if you are going to refer to a previous post, at least do justice to it and read the whole thing.
     
  20. Apr 21, 2009 #19

    f95toli

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    Re: Does quantum mechanical definition of momentum require "movement"?

    I agree that it makes sense (or at least is useful) when dealing with transport phenomena (which I also wrote in the other thread). But the question was if the definition of momentum requires movement, i.e. even when dealing with electrons in an atom. I would argue that the idea of something "moving" is more of a hindrance than a help in the latter case.

    However, it is worth noting that even in electronic circuits it is not always obvious what is actually moving. I did my PhD working with components where the quantized phase is the most "fundamental" variable (since charge isn't well defined because of the charging energy being so low). In most of the models I used (and sometimes still use) the equations of motions describe a phase "particle" moving around a potential landscape. One could of course argue that this is just a formal analogy, but this phase particle nevertheless behaves more or less the the same way electrons do in equivalent charge system (it can tunnel etc).
     
  21. Apr 21, 2009 #20

    alxm

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    Re: Does quantum mechanical definition of momentum require "movement"?

    I would say that yes, it does. I would say that movement does not require having an exactly defined position or momentum. (analogies abound) Something is 'moving' relative you if it has kinetic energy relative your frame of reference, and obeys Newton's laws of motions. This is true whether you're talking about classical or quantum mechanical particles. It's also implicit in how the QM definition/derivation of the momentum operator.

    Classical motion then, like all classical physics, then becomes a limiting case of QM. Classical particles obey Newton's laws of motion because quantum particles do so. 'Motion' in QM is not an analogy, it's the same thing.

    Or to put it another way: At which point in the transition from quantum to classical domains would you say that things start moving, then? And in what way is that motion fundamentally different?

    And I would say the opposite. Electron motion in atomic and molecular orbitals is usually referred to as such. Not 'motion' but as real motion. It's implicit, then, that you're not implying the kind of exact, stable trajectories of the Bohr atomic model. Anyone who's past the level of introductory QM knows that. Throwing out the concept of 'motion' just because the details of the Bohr model concept were wrong is overzealous.

    But if you do not think of electrons in an atom as moving, then you will have big trouble understanding the central and still-relevant problem of electron correlation. I.e. the quantum many-body problem. Which is not an analogy to the classical many-body problem. It's the same problem, and difficult for the same reasons. Using wave functions instead of exact coordinates complicates matters, but does not change the fundamental difficulty of it.

    This is an analogy: Electrons in a stationary state, have a time-independent location-probability distribution and therefore appear not to be moving, although they have momentum. Likewise, water flowing through a transparent pipe appears to be stationary, but is not.

    Defining motion as 'appearing to move' doesn't make sense; it would exclude lots of classical phenomena like standing waves. I see no reason to define 'motion' as requiring exactly-defined positions and momentums.
     
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