Double Slit experiment with just one photon or electron

Has anyone done an experiment where they send just one particle? (And end the experiment) Do you observe two points on the screen in that case or just one?

You don't observe two points - you get a probability. This is what the video was trying to indicate by showing dots on the screen. Those dots are the reason for postulating the role of probabilities in quantum mechanics.

The idea is that you can't predict where a single electron will hit the screen, the only thing you know is that some places are more probable than others. The probability is dictated by the probability density function which ostensibly can come from the quantum mechanical wave equation of the electron.

The probability distribution function for a single particle is the same function (aside from units/magnitude) as the intensity you see for a large number of particles. After all, that is always what we see when we observe the interference pattern. You just get enough particles that you can't distinguish single hits anymore.

Yes, several people have done the experiment, and the photons/electrons are not split, you can get one hit at a time. Here is a second video .

The wikipedia two slit article has a build up of the electron interference pattern one at a time.

It is a probability pattern that shows the interference. The electrons and photons either go through one of the slits or the other, whole. Nothing mysterious is happening.

There have been experiments recently where one can detect which the slit the particle went through and still the interference pattern appears.