Can a single particle be thought of as a wave?

I don't have a direct reference but I read that Dirac once remarked, “a photon can only interfere with itself”. But I recently came across a website in which it is written

The manifestations of wave-like behavior are statistical in nature and always emerge from the collective outcome of many electron events. In the present experiment nothing wave-like is discernible in the arrival of single electrons at the observation plane.

Is there a contradiction between the view expressed by Dirac and the view expressed in the website? Or am I mistaken?

• It is the probability of a particle being at (x,y,z,t) that has wave like properties, because it is given by $Ψ^*Ψ$ where $Ψ$ is the wave function . See these experiments with single particles en.wikipedia.org/wiki/… sps.ch/en/articles/progresses/… Dec 31, 2019 at 16:51
• You are mistaken: there is no contradiction. The wavy probability profile of a self-interfering particle may be best mapped by the statistics of several similar particles. Review your probability. Dec 31, 2019 at 17:16
• In order for your question to be answered, you need to specify what you mean by "particle" and "wave". If not then you will probably get different opinionated answers. For example, I really don't like when others talk about "particles interfering with themselves" and saying that a "wavefunction" means the particles are waves. But others on this site would disagree, and you can use the above language if you carefully define what you are talking about. Dec 31, 2019 at 18:40
• Cosmas Zachos, please read the linked page. The quote says that wave-like behavior itself, not just the mapped profile, emerges from the collective outcome... But wouldn't a single particle need to have wave-like behavior to self-interfere? Dec 31, 2019 at 19:56
• I am reading the statement for you, dropping the metaphysics. Behavior is a clumsy synonym for probability, which you may only map through collective outcomes. Think of flipping an uneven coin: even though each coin flip has the same uneven probability, only the collective outcomes will map it. This is exactly what Dirac emphasizes in his legendary QM book. Dec 31, 2019 at 20:28

No contradiction, actually. When you detect a particle you get one dot. For instance, x-rays directed at a crystal, which are scattered on to a phosphor screen and a camera records the image. X-rays, neutrons, or other particles can be delivered slowly enough that they visibly come one at a time. BUT... if you keep the experiment going long enough, if you record enough dots, you will see the diffraction pattern. If the particles are coming one at a time, but collectively show a diffraction pattern, they can only be interfering with themselves because there is nothing else for them to interfere with.

Here is an example x-ray diffraction pattern from Eastman Kodak. You can see how it is composed of individual pixels, each one representing one x-ray detection. And those x-rays came one at a time, they didn't come all at once and interacting with each other.

• Please read the page that I have linked to. The quoted section says that manifestations of wave-like behavior "emerge" from the collective outcome... So they are saying that a single particle does not behave like a wave. Is that not different from what Dirac said? Dec 31, 2019 at 19:49
• I thought I had addressed that when I said one particle detection produces one dot, and you need many particles before the diffraction pattern becomes apparent. So your quoted section is quite right, it IS a collective outcome. One dot doesn't tell you anything! I have added a sample x-ray diffraction pattern in the answer to illustrate that.
– Greg
Jan 1, 2020 at 18:16
• I suspect the OP’s confusion is in surveying probability with statistics. Jan 1, 2020 at 19:17

The fact that a beam of photons or electrons can produce an interference pattern with dimensions measured in centimeters, leaves no doubt that they have wave properties, and if you want to read a book on quantum mechanics you need to be comfortable with wave equations expressed as imaginary functions. The particle idea is associated with the fact that all of the energy and momentum of a “wave packet” (such as a photon) can be absorbed by an entity the size of an atom atom or smaller.

• It leaves no doubt that a beam has wave properties. The question is if a single particle has wave properties. Jan 1, 2020 at 19:42