The consistent interpretation of a double slit experiment indicates that the wave function of even a single electron must be spread over a macroscopic region at the moment when it hits the scintillating screen. The bright dots that appear on the scintillating screen during a position measurement of an electron is interpreted as an evidence that there must be a pointlike entity beside the wave function.
(see details of double slit interference experiment)This is however a wrong conclusion!
The solution of Schrodinger equation shows that the atomic wave functions are localized and that their average spatial extend is of the order of 10-8 cm . The bright dots indicate only that there occurs a transition from macroscopically sized wave function to an atomic wave function. There is no evidence that there is a pointlike entity inside/beside the wave function.
Wave function IS the electron.
The main problem: Why does the transition occur each time to the eigenstate of a different atom although the initial conditions are apparently the same.