Talk:Wave packet

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1 Wave packet image
2 Complete Rubbish Without Math
3 Wavepackets and metaphysics
4 Mathematics Section
5 Not Rubbish, but needs guidance
6 Question about image

[edit] Wave packet image

To those who felt the wavepacket representation image was confusing. I believe it is useful to have a graphical representation of a wave packet on this page. Any suggestions on how to improve the image to your tastes? Note that the "axis labels" of a wave packet are completely arbitrary. It depends on the representation one is working in, the point is the shape of the graph not the labels.

For now I'm restoring the image, so the site will be more clear. Let me know how to improve it, or upload a better one rather than just deleting content.

My main objection to the image is the totally ambiguous arrows. If the horizontal axes is position, then I would gather that the Position arrow is indicating the line (whereas its not clearly pointing to it), and then the momentum arrow is trying to indicate that the momentum is related to the width of the wave packet. The caption still does nothing for me, because it does not explain what the arrows are indicating, or that we are in position-space. I'll add to the caption, but it would be ever so much more clear if the image itself was made more clear. Laura Scudder 20:30, 17 Mar 2005 (UTC)

If you read the text the ambiguity in the position is supposed to demonstrate the uncertainty principle. What I was trying to illustrate is that the "position" is somewhat fuzzy, I'm not sure how else to draw it. I suppose I could remove the arrows? Not sure that this would be more effective though. Some sort of gaussian distribution overlay may work better? I'll have to explore some possibilities. John187 16:33, 18 Mar 2005 (UTC)

I understand the idea of not labelling the graph, since a wave packet looks identical in position-space and momentum-space... however, having a graph without any label on the x- and y-axis is really bad form. It's confusing to specialists and non-specialists alike, since it doesn't really represent anything (are you plotting amplitude vs. time (amplitude of what?), or time vs. distance, or length vs. mass ... or what?). Why not just have two pictures: one for position-space, one for momentum-space, and let the reader see how similar they look. And you don't need to label "position" if the x-axis is already "position"... it should be clear to the reader that the position is ill-defined, since a range of positions is included in the packet. --132.206.205.100 14:07, 15 Jun 2005 (UTC)

Simply removing the arrows would be worse without axes labels. Then it's just a meaningless graph. The optimum would be axes labels and, as suggested, plots in both position and momentum space to convey the relationship. And if there must be arrows in addition to axes labels, I think instead of momentum and position, it'd be preferable to be clearer and choose for instance δp, δx. I would just do this myself, but I currently lack ability to generate acceptable quality pngs. --Laura Scudder | Talk 16:19, 15 Jun 2005 (UTC)

This discussion of wave packets seems almost completely based on their interpretation in quantum mechanics, and contains little discussion of generic properties of wave packets. The simplest example that I can think of is the complete lack of information on the group velocity, a concept that is both a general property of a wave packet and is a part of nearly every subject that works with waves and wave packets. The current organizational structure makes it difficult to include such information.

[edit] Complete Rubbish Without Math

If this article doesn't include math, or links to a more mathematical article then it is complete rubbish. Metaphysics should be in a wholly separate article and not included in wave packets. These are not only quantum phenomena, they are mathematical outcomes of waves. Please for the sake of wikipedia clean this article up. I don't want to insult the gracious individuals who have made this article but it is incomplete and misleading. More math please, less junk philosophy!

Wikipedia is produced by volunteers, and I personally don't understand the math you describe. Are you volunteering to provide the improvement you describe? If so, let's see what you had in mind. If not, do you really think your attitude is what will get people to happily pitch in and fix it? Art LaPella 01:33, 14 November 2005 (UTC)

[edit] Wavepackets and metaphysics

It seems rather odd that an article on wavepackets is about 50% on metaphysics...the article itself reads almost like an opinion piece. I'm going to put an NPOV tag on it; this page also needs some cleanup I think. --HappyCamper 12:39, 12 January 2006 (UTC)

I don't understand the science very well and you may be right about too much metaphysics, but I do have an opinion on unexplained tags. What opinion is over-represented or under-represented? I didn't notice any typical cleanup problems like spelling or grammar. Art LaPella 21:42, 12 January 2006 (UTC)

For example, for me, the first sentence is far too loaded: "The wave packet is one of the most widely misunderstood and misused concepts in physics." Also, at minimum, it should mention some of the influences that de Broglie had on this concept. This name is currently absent from the article!

Well, I suppose it would be unfair of me to add those tags, but for some of the articles that I found, I added these two, and after 9 months everything was fixed up. You can remove them if you like, as I probably won't get a chance to add more mathematical detail to this anytime soon. :-) --HappyCamper 22:04, 12 January 2006 (UTC)

Better. Art LaPella 02:13, 13 January 2006 (UTC)

As far as I'm concerned the metaphysics section could be cut back. I haven't done it myself yet because I'm scared of only leaving some disconnected nonsense and making the situation worse. — Laura Scudder ☎ 23:55, 17 February 2006 (UTC)

I have to say, I'd rather not see any reference to metaphysical concepts on this page. Consider it a personal bias if you will, but I think a subject that is fundamentally scientific in nature is serriously comprimised when metaphysics are included. I propose a rewrite, of a few of the paragraphs at least, it tends to read like a 10th grade science essay rather than an encyclopedia article. For instance, the first sentence should be eliminated altogether, it does't really add anything but ambiguity to the article. But thats just my $0.02. Davepetr 20:11, 17 February 2006 (UTC)

10th grade may be aiming a bit high... if it's possible to write an article in a simpler form that's equally accurate, let it be so. As far as the metaphysics section goes - a lot of that is just really bad logic, and I'm going to weed some of it now. Pjrich 06:10, 1 March 2006 (UTC)

[edit] Mathematics Section

I am starting to put in a mathematics sections and some relevent diagrams. It is going to take place over the next couple of weeks. If able, feel free to make corrections or additions. --Nkrupans 06:13, 20 January 2006 (UTC)

Sorry for editing the front page. My comment should be placed here:

Let me add a little comment without which above-mentioned derivation would be hard to comprehend by most people myself included. Not everybody has simply patience to solve puzzles each time he or she tries to learn anything about quantum mechanics. This differential equation has a simple and useful solution in the form of something close to Maxwell distribution:

$A(k) = A_{0}\exp[-\frac{1}{\sqrt{2\pi}}\left(k - k_{0}\right)]$

where Ao and ko are constants.

greg_park_avenue

[edit] Not Rubbish, but needs guidance

Okay... Wikipedia is a fascinating eperiment, but if anything it is an attempt to harness to energy of lots of people to explain a lot of things in a short amount of time. I am only one person, and I happen to be a physicist, and I don't have the time to go around rewriting every basic physics article that I find in serious need. In the spirit of the grand experiment what I can do is offer some guidance and maybe release some of that vast reservior of energy. So, here goes:

A wave packet per se is just a superposition of individual wave solutions that produces a localized packet by operation of superposition of the individual components arranged so that it reinforces at the center and interferes increasingly towards the extremes. The article is more or less correct in conveying this despite that it goes astray in the details. This can be fixed. However... we need to reel in the diversion about collapsing wave packets. One of the major intrigues of quantum mechanics is the so-called collapse of the wave function -- not the collapse of the wave packet. Well, maybe we can think about collapsing wave packets too, but that is not what you are thinking about when you are learning quantum mechanics and contemplating its postulates. Please go check this out by reading up on basic quantum mechanics and then see if you agree that collapsing wave packets is not what you want to convey as an example of what happens when you measure something. A wave function can be a superposition of states each of which is an eigenfunction of some operator with associated eigenvalues and these functions need not be waves as you usually think of them and need not be assembled into a packet. A measurement does produce only one eigenvalue as the result and so we describe the result by saying that the superposition collapsed to just one state -- in which it can remain for awhile. In this context we are talking about the state of a system of some kind and, in principle, a system can exist in a superposition of states distributed in a way that maps the probabilities for it to "collapse" into one of them upon measurement. The superposition of states is analagous to the superposition of things in a wave packet -- but is a much more general concept. Bound states, for example, are not visualized the same way as propagating packets.

Contrast this with the simple idea of a wave packet. A wave packet is a superposition of -- well, waves! Okay, waves can be solutions to quantum mechanical problems, but you don't need to invoke quantum mechanics as such to have waves or wave packets. It is also true that we worry about how to more realistically describe how particles propagate and since waves correspond to (mostly) freely propagating particles the packet becomes a model for this to some extent. In that context we get some real insights and it is those insights that I think the article should focus on.

My recommendation is that one or two contributors go and grab an elementary quantum mechanics textbook or find some online course material and then find within that some discussion of wave packets and see how they get introduced and for what purpose. Study this deeply and put it into your own words -- but be careful to stay on topic before you suggest the possible connection to other ideas. Maybe even before indulging the world of the quantum, just pick up a math physics book or find some online course material and see if they describe wave packets there.

Can you produce an article that answers basic questions like: what is compulsory about the shape of the packet or distribution of the coefficients as a function of the wave number k? Is there any arbitrariness in the shape? What keeps the packet from falling apart as it propagates? What happens if the wave number k is not proportional to angular frequency (i.e. becomes dispersive) and when does this happen in practice? Can someone upon reading the article grasp at least one example of Heisenberg's Uncertainty principle applied to wave packets?

Sorry for resorting to pedantry, but writing a really good article is real work no matter whether the topic is basic or advanced. Maybe another expert can drop in and spend more time -- maybe even someone with particular expertise appropriate to this topic. My goal was to point out that whoever is working on this needs to do more study -- but should be allowed to do so and I am confident as much help as necessary will show up. If they are good readers they might not need much help and experts can just tidy things up at the end. --scanyon 09:48, 8 June 2007 (UTC)

Rather than ask amateurs to study your subject until they know it as well as you do (their time might be better spent repairing millions of simple problems summarized at Wikipedia:Community Portal), you might choose one or two interesting physics articles that you find in serious need, and rewrite with references (so we know whom to believe). Then someone like me can clean up the typos and such. Art LaPella 22:02, 8 June 2007 (UTC)

I am not being patronizing when I suggest that I am confident that whoever made major contributions to this article demonstrates enough competency to correct the problems with just some guidance and study. Also please accept that I am personally already engaged in a major revision to a math article which touches upon some things I have an interest in and is rated by the powers that be as having high priority. I need to finish an existing commitment using available time before becoming too involved in another one. This is kind of fun, but its also very time consuming. Then also believe that you do not have to master physics to do an article on wave packets. You do need to do some reading and take some guidance. Its not really an advanced topic. Finally, though, in rummaging through Wikipedia-physics I have seen plenty of physics expertise at work which exceeds my own talents so I know its available and I am not at all trying to be patronizing by declaring that I "don't have time" to do this as if I could save you but I'm too busy to care. The reality is that I care, but genuinely don't have the time that I think this deserves. Besides, in my general experience, the time you invest in figuring out what went wrong here will strengthen you and educate you at the same time. If you poked your nose in this in the first place you must have a desire to master something and this is your chance. There is no more powerful tool for achieving mastry than struggling to explain something clearly. Fortunately for you guys, the web is full of wonderful free course material and all you need is time and curiousity to find it. Of course, there is also still the old fashioned way -- go find a book or two in a library or bookstore. You are on the right track, just follow the leads that I and other like me provide and I think it will turn out fine. Leave me occassional notes on my talk page and I will see what I can do to help as you go forward. --scanyon 06:36, 9 June 2007 (UTC)

Looking through page history, it appears that "whoever made major contributions to this article" (my career is financial) and in particular to the section you disagree with, is User:John187 and perhaps User:Nkrupans. Those editors have made only 2 edits each to Wikipedia in 2007, and no edits to this article, so neither is likely to be reading this. Art LaPella 23:09, 9 June 2007 (UTC)

Hmmm... well, what is your feeling about just deleting the digression on "collapse of packets" for now and seeing who becomes unhappy about it? I am quite new to the Wikipedia process, so I am hesitant to delete other people's work without discussing it with them. In the customary scheme of things, though, deleting and reverting are the most direct ways of contesting correctness of material and the worst that can happen is you upset someone enough that they come back and make a case for themselves. If that is the way the system works then so be it. On the other hand, it would be nice, at times, if a pool of experts could be distinctly queried from time to time in an effort to recruit help on a specific matter. Maybe there is such a mechanism and if so you could explain it to me.

And by the way, the math as shown is okay except for the last step, but is not presented in as general or explanatory a way as I think it should be. I can take care of this for you later, but there are worse problems. There are, as I hinted in the first set of comments, lots of things that can be said about the parameters used to describe a specific wave packet and its behavior in a set of circumstances. To the uninitiated, the central questions that take thought to answer are: just how does a wave packet come about and what factors determine its shape -- or equivalently, the distribution of k values? Is a propagating electron reasonably described by a wave packet (this *is* a question with quantum theory implications) as we would expect a light pulse to be? The mere fact that I can build a mathematical structure does not mean it is a valid description of what happens in nature or by engineering. Where do we see (or think we see) wave packets? If we set about to make our own (is this pulse shaping?) when and how do we do that and for what purpose? For someone like me, the math is no problem. I can also discuss some of the motivation in general terms, but the best expert would be someone who literally deals with wave packets -- maybe an optical physicist or engineer -- maybe someone who does interferometry for a living. Again, I can bore you with the details of the math later on. Its the motivational material that takes more scholarly research to do it justice. Building a bibliography will take a little time.--scanyon 04:49, 13 June 2007 (UTC)

I have 8895 total edits on Wikipedia. You have done more than enough to justify "deleting the digression" (I'm speaking procedurally, not commenting on the scientific merits). This is especially true because the text I think you want to delete doesn't have any supporting references in the text, and may therefore "be removed" (Wikipedia:Verification). Anybody who doesn't like the text being deleted now, should have shown up last week. But if you want to discuss this with a pool of experts, try Wikipedia talk:WikiProject Physics. Art LaPella 07:45, 13 June 2007 (UTC)

Okay, I spent some time looking into this in order to more clearly and succinctly state the problem and contemplate how deleting material can be justified. Please look this over and then confirm your agreement about what should be deleted at this time.

The article is about wave packets. As a mathematical construct, wave packets do not require appeal to quantum mechanics in order to be defined. It so happens that in a quantum mechanical context solutions to Schrodinger's equation can be waves as they are normally conceived and in all cases superpositions (linear combinations) of solutions are solutions in the aggregate to the Schrodinger's equation. Since wave packets are, by definition, superpostions of waves that result in a localized wave form, it is possible to construct a wave packet of solutions to some quantum problems. This results in a way to demonstrate Heisenberg's Uncertainly principle concretely, but something similar can be demonstrated with respect to wave packets even without resorting to a quantum scenario. Now, in a qauntum context, wave packets are a way to construct a localized solution for free particles consistent with some particle characteristics in cases of moving particles. Light is known to be quantized into photons and it becomes possible to model light and electrons alike using packets formed from solutions to the free-particle situation -- and they move as they should in a vacuum and display dispersion in media as the wave packet model would predict. Now stop for a second. We got to quantum mechanics becuase we wanted to show an important example of something. Quantum mechanics was not needed to define wave packets, but wave packets play a role in quantum mechanics -- of course so do differential equations, Hilbert spaces and lots of other things. That does not mean in a basic article about wave packets we need to explore all those topics in depth.

In sections 3, 4, 5 and 6 the article takes off into the quantum world with a vengeance. Some statements made are related to the main topic, some statememnts are poorly made or made without adequate context. There is a preoccupation with "collapse of the wave packet." There is, indeed, a central postulate in quantum theory about what happens when you take a measurement of a system in a state that is a superposition of basic solutions (eigenstates or eigenfunctions of the measurement operator) and that postulate is often described as "collapse of the wave function." Okay, a wave packet is a wave function of a particular sort and in the quantum context we could impose a measurement on it and precipitate a collapse. Packets are complicated things in some contexts, however, and there is even a notion of reviving collapsed wave packets. Does this create enough relevance to justify section 4 in particular? I don't think so -- but that is just my opinion.

There is more. If you google long enough you will discover that some authors are sloppy about using "packet" terminology. I did not do a scholarly survey, but it was clear that its fairly common for authors to lapse into calling ANY superpostion of states a packet -- but this is patently inappropriate unless you are referring to a resultant wave form which demonstrates a localization. I suspect that whoever wrote sections 3, 4, and maybe 5 encountered this and failed to comprehend the history and the distinctions that would have indentified this as a departure from well defined ideas.

There is even more. In googling I discovered that the current Wikipedia article on wave packets is often quoted as authority in the context of discussing 'collapse of the wave packet" -- so we are contributing to a problem instead of contributing to clarity! Enough already. I am going to delete sections 3, 4, 5 and 6. Let the chips fall where they may.--scanyon 07:57, 14 June 2007 (UTC)

(addendum) In the cold light of morning I have edited out a reference above to an uncited article which I suggested was a case where a professional author referred to something as a wave packet that was not. Although the english in that paper was not at full fluency, I reread it this morning and, despite some conceptual conundrums that haunt all experiments of this type, he was correct as far as he went. Fortunately I did not malign him by directly citing the article. Still, the abuse sometimes happens -- as I think it did in the article -- and the key point is that collapse of the wave function is the general issue and wave packets are just a possible case. In the case of wave packets per se, the collapses most notoriously explored often involve a collapse of the indeterminancy of some property of the particle -- like spin or polarization. The more general case of collapse is what is fundamental, but there is fascination with packets that shows up often owing to a mystical attraction to quantum mechanics. Quantum is truly counterintuitive, but why and how need to be explored elsewhere -- in which case the ability to make reference to a compact description of wave packets per se will prove helpful.

Lastly -- with sections 3-6 gone what I think should ultimately happen is that appropriate mention should be made of the fact that wave packet formalizations are important in quantum mechanics because they provide a way of modeling localization of particles. I just don't think a full-blown exploration of some otherwise interesting aspects of quantum theory are appropriate here and I more stongly believe that distracting readers into thinking that wave packets are a qauntum phenomenon per se is a disservice. --scanyon 16:23, 14 June 2007 (UTC)

As best I understand the above, sometimes it says that the deleted sections were irrelevant to an article about wave packets, and sometimes it says that the deleted sections were largely wrong. If they are right but irrelevant to this article, I hope you have considered the alternative of merging any useful information with an existing article such as Wave function collapse, or starting a new article with it. Art LaPella 02:28, 15 June 2007 (UTC)

Hmm.. I suspect what you are perceiving is a residual discomfort on my part for having deleting the material. What is true is that some of the material deleted was correct as far as it went, but was poorly connected to the main topic. My gratuitous comments about some of it needing to be better clarified by establishing a firmer context is true, but probably superfluous at this point. My afterthought was meant to move somewhat in the direction you are suggesting. In any case, I think the deletion was appropriate and that moving that way requires a fresh start. I strongly agree that subsequent attempts to redeem some parts of the deleted material need to include references to available related articles and Wave function collapse would be among them. It is certainly true that wave packets are utilized in quantum theory, but if you look at any textbook or monograph on quantum -- starting with Dirac's own "Principles of Quantum Mechanics" you will find that it is not an extensively considered topic. Accordingly, the article should focus on explaining wave packets per se well and then providing a link-rich, but succinct discourse that connects the explanation to its applications in quantum theory. Within the context of quantum theory it might be appropriate to have a subarticle on quantum wave packets. I will try to do something about cleaning up the math within a week and will do so in a way that sets the stage for what we agree should follow. As some folks in previous discussion have complained, the topic is essentially a mathematical one and perhaps one reason it got off on a tangent was that the needed mathematical depth left it otherwise empty ... but that's just a theory on my part. --scanyon 18:14, 16 June 2007 (UTC)