What keeps electrons spinning around their nucleus?
in [Relativity]
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From: Bilge on 30 Mar 2005 04:30 puppet_sock(a)hotmail.com: >dubious(a)radioactivex.lebesque-al.net (Bilge) wrote in message news: ><slrnd4dc08.n0h.dubious(a)radioactivex.lebesque-al.net>... >> Nick: >> >What is the velocity of an electron in a shell? >> >> Velocity isn't a quantum mechanical observable. > >Of course it is. What ever do you think you get when you take >the time derivative of position? You get eherenfest's theorem, in which expectation values become classical variables in the classical limit: (d/dt) <f|x|f> = <df/dt|x|f> + <f|x|df/dt> + d<x>/dt Since i\hbar df/dt = -(\hbar^2/2m)\grad^2 f, you can substitute for df/dt, do some arithmetic and obtain the classical limit: v = d<x>/dt so, it's a velocity if you replace operators by the time derivative of an expectation value of the position. An expectation value isn't an hermitian operator, so it isn't an observable. If you want to try defining the ``operator'' dx/dt, then: E = i\hbar d/dt => d/dt = (-i/hbar)E, so dx/dt would be the operator (-i/hbar)Ex.
From: Bilge on 30 Mar 2005 04:35 Creighton Hogg: > > >Ah, I think the difference here is that others are probably using the term >observable the way I would use it: an operator that commutes with the >Hamiltonian. Actually, the problem is referring to the time derivative of an expectation value as an observable. The so-called velocity one can obtain quantum mechanically is given by ehrenfest's theorem as a classical limit by identifying v = d<x>/dt = <p>/m as the classical variable.
From: Bill Hobba on 30 Mar 2005 04:38 <mmeron(a)cars3.uchicago.edu> wrote in message news:Zcr2e.42$45.5559(a)news.uchicago.edu... > In article <lrm2e.17108$C7.9311(a)news-server.bigpond.net.au>, "Bill Hobba" <bhobba(a)rubbish.net.au> writes: > >> Seeing how Landau wasn't above > >> mentioning both centrifugal and coriolis forces in his Mechanics, is > >> see no reason for purism here. > > > >He sure did. But notice he makes it clear they are the result of using non > >inertial frames to write the lagrangian in. > > > Did I (or anybody else here) said otherwise? Sorry Mati - it is obvious I did not express what I wanted to say well enough. I was not questioning anyone thinking or saying differently - I was simply passing a comment. Sorry for any confusion. Bill > > Mati Meron | "When you argue with a fool, > meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: Bilge on 30 Mar 2005 04:46 Tom Capizzi: >I have heard that the evidence for glass flowing is not reliable. It doesn't >happen very quickly, so it originally came from examination of old glass. >The old glass was found to be thicker at one end. The assumption was >that it flowed. However, it was later shown to be an artifact of the way >glass used to made, by spinning large sheets of it. Has anyone else heard >similar reports? Even if true, I'm not sure that it's relevant. Lots of materials flow under pressure. For example, the copper gaskets used for conflat flanges, which are sort the ultimate in vacuum seals, depend upon the copper to cold flow when you tighten the bolts to acheive a vacuum seal, but no one treats copper as a liquid. I imagine that anything would flow under its own weight if the piece of material had the right dimensions, i.e., long, not very wide, thin and then stood on its short edge.
From: jmfbahciv on 30 Mar 2005 06:00
In article <f1l2e.34$45.5068(a)news.uchicago.edu>, mmeron(a)cars3.uchicago.edu wrote: >In article <pPmdnT872IUW8tTfRVn-rw(a)rcn.net>, jmfbahciv(a)aol.com writes: >>In article <7K52e.21$45.3808(a)news.uchicago.edu>, >> mmeron(a)cars3.uchicago.edu wrote: >>>In article <Xns9627C5AEB62D6WQAHBGMXSZHVspammote(a)130.39.198.139>, bz >><bz+sp(a)ch100-5.chem.lsu.edu> writes: >>>>mmeron(a)cars3.uchicago.edu wrote in >>>>news:8B12e.18$45.3391(a)news.uchicago.edu: >>>> >>>>> In article <Mo12e.16031$C7.902(a)news-server.bigpond.net.au>, "Bill >>Hobba" >>>>> <bhobba(a)rubbish.net.au> writes: >>>>>> >>>>>><mmeron(a)cars3.uchicago.edu> wrote in message >>>>>>news:XQ02e.15$45.3352(a)news.uchicago.edu... >>>>>>> >coordinates, but I think what is misleading is to call the >>correction >>>>>>> >terms "forces". >>>>>>> >>>>>>> Only if you attach more meaning to the term "force" than it deserves. >>>>>> >>>>>>Ahhhhhh. Yes. As Feynman says it is half a law. It gains its full >>>>>>meaning when combined with other laws and/or concepts such as Coulombs >>>>>>law or the introduction of non inertial reference frames. >>>>>> >>>>> Yes, it is a rather complex issue. I wrote some stuff about it in the >>>>> past, here, but I never kept a copy. But it certtainly needs some >>>>> sort of broad framework, to make sense. >>>> >>>>Especially when someone keeps insisting that force is always the result >>of >>>>acceleration >>> >>>Cause, not result. >>> >>>> and that without acceleration (as for example when a gyro >>>>precesses at a constant rate, or when a mass moves at a constant velocity >>>>because it is overcoming drag or friction) there is no force and no work. >>>> >>>Where there is net force, there is acceleration. The F in Newton's >>>law is the total (i.e.) net force acting. Since forces are vectors, >>>it is perfectly possible to have different non-zero forces to sum up >>>to a zero net force. >> >>This is why using algebra in first physics courses hurts learning >>more than it helps. >> >I don't see why it should hurt. Of course, it is better if you can >use calculus, not just algebra. Oh, it hurts because the concept of changes doesn't show up when doing the math. I like the integral or derivative glyph to keep reminding me which an equals sign doesn't. High school algebra only spends two or three pages on inequalities and ranges, IIRC. /BAH Subtract a hundred and four for e-mail. |