Talk:Matter wave

Proposed new section: Special relativity and de Broglie's phase harmony

Some time back we deleted a section we did not understand. It concerned me that that it quoted de Broglie's thesis.

While working on the phase velocity section I read more of de Broglie's original work. His famous work includes a simple but consequential application of special relativity. To me the combination of wave-particle QM and special relativity in a historical context is simply too notable and appropriate for reader of Wikipedia Physics to let go.

I have resurrected the section in spirit but completely re-wrote it and built a figure to aid in understanding.

I am looking for feed back. I've already decided to add a light grey x-axis. Other suggestions on the figure welcome before I go through the tedious edit cycle for it.

My goal for this section would be that someone with a little understanding of relativity and a little of wave-particle duality would come away knowing that these are, surprise!, deeply connected. Johnjbarton (talk) 23:15, 6 June 2023 (UTC)

The intuition behind de Broglie's insight seems to be straightforward (as from the originally deleted section that you linked). The animation in your sandbox does not help (at least, it is opaque to me). I also find the new wording obscures insight. Here is how I think of it: when the observer is in the particle's rest frame, there is a phase that is the same everywhere but linearly increasing with time (though the amplitude might be localized, e.g. in a Gaussian spatial distribution). In a Galilean framework, a moving observer would see everything still in phase everywhere, just with the distribution peak moving (the original observer's axis on which his origin moves, i.e. his time axis, is just tilted). In special relativity, the time axis also tilts, but the plane of t = 0 also tilts by the same amount, with an associated squeeze transformation at 45°. The moving observer's t = 0 plane now cuts through the planes of constant phase, producing spatial oscillations (nonzero wavevector). A simple space–time diagram wit these two conditions next to each other would be able to illustrate this easily. No need for any formulae. —Quondum 00:01, 7 June 2023 (UTC)

While an alternative point of view is an interesting topic, my goal was only to report de Broglie's point of view in a way that can be related to other wikipedia articles. Obviously that was not successful. Johnjbarton (talk) 02:21, 7 June 2023 (UTC)

Since I have not done any hard-core relativity since undergrad, I honestly have no clean idea what either of you are referring to -- which suggests that a better explanation is needed of the relevance. (I assume that there is something more than the existing 4-vector representation.)

N.B., it may be that this connects to relativistic inelastic scattering and Cherenkov and similar, but now I am speculating. Ldm1954 (talk) 02:39, 7 June 2023 (UTC)

This is just a 4-covector. In special relativity, a scalar function of spacetime ψ(x^ν) = exp(iωt) [where ω is a constant, t = x⁰, and x^ν is the 4-position] necessarily takes the form ψ(x^ν) = exp(ik_μx^μ) for a constant 4-covector k_μ. This is a direct directly fits "by cause of a meta law of Nature, to each portion of energy with a proper mass m₀, one may associate a periodic phenomenon of frequency ν₀", with a modern restatement de Broglie's subsequent wording. —Quondum 11:02, 7 June 2023 (UTC)

What you say may be perfectly valid but there's too many unconnected dots for me. I don't think "just a 4 co-vector" will work for many readers, even if it is correct and minimal. Johnjbarton (talk) 16:50, 7 June 2023 (UTC)

Your comment reinforces my sense that we should do something to clarify that matter waves are a direct consequence of special relativity. @Quondum implies this is common (physics) knowledge, but I only came across the connection in the context of editing this page.

To be clear, this is not a 'relativistic effect' in the normal sense of $v\rightarrow c$. Rather, the de Broglie wavelength does not manifest at all unless there is some relative velocity.

Rehashing de Broglie's (rather lame) arguments may not be the best way to accomplish this, but I do not have access to better citable alternatives. What might the matter wave be telling us of the nature of matter? covers the topic with many citations to others, but I don't think it reaches the bar for citation. Johnjbarton (talk) 16:43, 7 June 2023 (UTC)

To me matter waves come from QM. I don't think QM comes from special relativity. Also, a particle in a box has a wavevector but no group velocity or probability flux (standing wave). If I remember his thesis right, de Broglie was also thinking about standing waves. Ldm1954 (talk) 16:50, 7 June 2023 (UTC)

It's 'just' the (observed) wavelength that comes from relativity. A stationary matter wave has no wavelength (or the wavelength approaches infinity). The phase is just rotating at the same value in all space. With motion the observed phase varies with space, the variation depending on relative velocity. It's both profound and trivial. For example, the phase of a particle stationary with respect to a detector has no consequence AFAIK. Johnjbarton (talk) 17:26, 7 June 2023 (UTC)

A matter waves cos(2\pi k.r -E*t/hbar) has a wavevector k, a wavelength 1/|k|, time dependence and no probability flux. A matter waves exp(2\pi ik.r - qz) is evanescent along z with no probability flux in z, only x and y. Currently there is not (IMHO) adequate coverage here of anything beyond fully travelling waves. Ldm1954 (talk) 17:40, 7 June 2023 (UTC)

Even the link above given by Johnjbarton, despite giving a reasonable analysis and insight, devolves into formulae with gammas and so on, which is not likely to impart insight to the average physics-oriented reader. But it does seem to think that de Broglie was not able to think holistically about this idea, so for the purposes of the article, such an insight would have to be presented as subsequent development of de Broglie's conception. The confined scalar wave R(r) exp(iωt)) [r being time-independent on the stationary observer's frame] has the potential of being simple to present and demystifies the phase and travelling velocities without needing gammas to present. This is valuable to a reader and clearly referenced, but I leave it to you decide whether/where it belongs in this context. —Quondum 11:47, 8 June 2023 (UTC)

Yes that is also my assessment: pluses and minuses. The Shanahan article amounts to (re)-interpretation: very interesting but at the current stage it does not predict results that can be verified. For now I think set this aside until I can read more. Johnjbarton (talk) 16:43, 9 June 2023 (UTC)

Standing matter waves

Thinking of standing matter waves as a separate class seems to me to be erroneous. That would be saying that the standing modes of an electromagnetic wave form a separate class, whereas it is simply an emergent phenomenon given boundary conditions imposed on a travelling wave: it is just a superposition of travelling waves. In this context, multi-particle waves do not appear to behave as a superposition: the wavevector is determined by the total mass (or perhaps a more complex description). —Quondum 12:53, 8 June 2023 (UTC)

Also, the connection between the effective mass for standing and travelling matter waves is the same in all cases -- via the second derivative, it does not matter whether they are quasiparticles or not. Ldm1954 (talk) 02:33, 9 June 2023 (UTC)

May I suggest that standing matter waves are not analogous to electromagnetic standing modes? AFAIK the latter are purely different boundary conditions. But standing matter waves are idealized models for bound quantum systems where forces alter the waves rather than boundary conditions. We talk about "particle in a box" not in comparison to blackbody radiation but in comparison to hydrogen.

In fact half of de Broglie's original punch was his application of waves to Bohr atoms. Turns out that his treatment did not make the cut, but it was a thing and lit a fire under Schrodinger.

To further this section we need to make contact with matter wave concepts in chemistry. Johnjbarton (talk) 16:54, 9 June 2023 (UTC)

Agreed, what I added was just a stub on that. Ldm1954 (talk) 16:57, 9 June 2023 (UTC)

Sorry, no, standing waves have zero probability flux (group velocity is a less accurate term), and as such are fundamentally different from travelling waves which have a probability flux. Indeed, de Broglie connected hydrogenic states to standing waves in a ring, without doing the detailed math.A case can be made that most eigensolutions such as hydrogenic are standing waves.

Ldm1954 (talk) 02:20, 9 June 2023 (UTC)

I'm sorry that I opened this discussion. I cannot work with this style of argument. —Quondum 10:44, 9 June 2023 (UTC)

My apologies if I came across too strongly, but there are deep differences and this matters. Probably overkill, oversimple:

A travelling matter waves is going from A to B; a standing wave such as a particle in a box is not moving. Both have energy, effective mass and wavelength. Both are eigensolutions for different classes of problems, one free and the other with extra conditions.

For a free travelling matter waves, exponential, one can superimpose different wavevectors of the same modulus -- this is what one has in matter wave elastic diffraction. One can consider the small probe formed in scanning systems as an emergent phenomenon, as it comes from combining many waves. For a matter waves in a box you have to use cos/sin terms, you cannot separate the exponentials -- it is not emergent. Ldm1954 (talk) 12:39, 9 June 2023 (UTC)

My purpose with this thread was not to trigger a debate. Reconciling our perspectives would be nontrivial. —Quondum 13:19, 9 June 2023 (UTC)

"Part of a series of articles about Quantum mechanics"

A box on the right side of the page says: "Part of a series of articles about Quantum mechanics". And yet expanding each of the sub headings inside of the box never shows a link to matter wave. Is that intended? Johnjbarton (talk) 22:55, 11 June 2023 (UTC)

Good thought. I posted on the relevant page, so let's wait for responses. If no or favorable response, consider editing the template. Ldm1954 (talk) 04:26, 12 June 2023 (UTC)

New section ready for review: Matter waves vs. electromagnetic waves (light)

A new section in my sandbox is ready for review: Matter waves vs. electromagnetic waves (light). More can be done but I think the content is useful as is. As throughout this is summary material for other pages (which themselves need work, some of which I have invested).

Please edit there or comment here and let me know what you think. Johnjbarton (talk) 02:02, 17 June 2023 (UTC)

I put in some comments. While parts may be OK for atom optics, I know they are not for electron. I am not the best person to ask for those, but I could ask some of the real experts for some writing. Ldm1954 (talk) 03:07, 17 June 2023 (UTC)

Great comments, I'll work on them. Thanks! Johnjbarton (talk) 14:45, 17 June 2023 (UTC)

I finally got back and fixed up the draft. I made changes for each comment except the one on dispersion. The text already says 'vacuum' a couple of times so I left it as is, with a "?" for the response.

The change I made for coherence may not satisfy, but all I want to get across in this summary is 1) coherence is thing that applies to waves and thus to matter waves 2) it overlaps but does not equal optical coherence. And do this with references.

Please take another look and thanks again for the great review. Johnjbarton (talk) 16:50, 24 June 2023 (UTC)

Just back from travel, please give me a few days. Coherence with electron waves is a well researched topic, as it is critical to $N million electron microscopes. I will write something, plus get some input from friends who build microscopes. Ldm1954 (talk) 14:00, 25 June 2023 (UTC)

I published this section with some small additions. I found an online P. Hawkes book with two pages on coherence and boiled it down two one sentence ;-) I've been looking for P. Hawkes Principles v3 but I guess I will need to visit a UC library to read it, but I think that level would go in an electron optics article anyway.

Resolved

Johnjbarton (talk) 00:13, 7 July 2023 (UTC)

I never got around to looking (I was buried with making Triboelectric effect sensible). It looks good, I am not going to tweak and make H. G. Wells roll over in his grave. Ldm1954 (talk) 18:23, 14 July 2023 (UTC)