I have read that electrons fired individually through a 2 or more slits still form an interference pattern. I think this may be due to the fact that moving electrons produce electromagnetic waves (like in a transmitter aerial), and EM waves move electrons (like in your TV aerial). While each electron can only pass through one slit, the wave it produces could pass through all slits simultaneously, forming an interference pattern. Could the individual electrons be getting deflected by their own EM wave and following the beams to form a pattern?
Here is the experiment:
Electron buildup over time
The quantum mechanical scattering problem is "electron of given energy scattering through two slits a given width and distance apart". The electron is modeled by a complex number wavefunction solution with these boundary conditions. It is an elementary particle in the standard model of particle physics.
It is called a particle because when impinging one by one it leaves the footprint of a particle , as in the top frame, and then the accumulation gives the probability distribution for finding an electron at the (x,y) of the screen, which shows wave like interference. That is the real valued $Ψ^*Ψ$ probability distribution.
While each electron can only pass through one slit, the wave it produces could pass through all slits simultaneously, forming an interference pattern.
You are trying to solve this using classical physics erroneously because the electron is not radiating when approaching the slits. Its electric potential interacts within the quantum mechanical equation to the spill over electric fields of the walls of the slits, and thus it interacts with the slits and the wavefunction carries the information, similar to the way the hydrogen wavefunction carries the information of the electron orbital.
The quantum mechanical mathematical model became necessary in order to fit the data in the microcosm, and the data cannot be explained with classical interference, which carries energy and is measurable. The interference is in the probability distribution of the double slit.
It has been shown that the classical framework emerges from the quantum mechanical, and that the other way around does not work consistent with special relativity in any type of complicated models.
(actually in quantum mechanical field theoretical approaches, the electron passing through the slits interacts by exchanging virtual photons, but this is a subject you have to study quantum mechanics in depth to understand)
Particles which are deflected by their own wave function sounds very similar to the deBroglie picture of the pilot wave.
In the single particle experiment, the interference is said to arise because the particle is acting as a wave, instead of thinking it is in a particle state. You observe the particle, the interference pattern dissolves.
In the deBgrolie picture of the pilot wave, both the wave and the particle is present. This can lead to interesting phenomenon, such as the empty wave, which suggests a wave can travel in space but have no energy.
The wavefunction of an electron is intrinsic and dependent on its mass and momentum; it does not have any important connection to the electron's electromagnetic field, at least in the context of a double-slit interferometer.
The electron's wavefunction, which represents (the square root of) the probability density for finding the electron at any given place and time, actually passes through both slits. When the electron is detected, it is detected at one point location so does not produce an interference pattern. But when the detected locations of a lot of individual electrons are plotted out, you will see the interference pattern in the plot.