# 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/… – anna v Dec 31 '19 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. – Cosmas Zachos Dec 31 '19 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. – BioPhysicist Dec 31 '19 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? – Zachary Dec 31 '19 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. – Cosmas Zachos Dec 31 '19 at 20:28