If I put a sensor nearby the double slit to observe the electron’s flight path, the measuring devices presence will disturb the wave function of the electron and the wave property of the electron is going to be lost. The pattern is going to be the same as with solid particles (which de Broglie wavelength is longer than the distance between the slits) – no interference between particles and they form two intense lines behind the both slits.
(I know this from my bachelor’s studies, but still this concept is bit weird. For the wave function to be disturbed I tent to think that the measuring device needs to be interacting with it’s environment. How would even one measure electrons position without direct charge collection?).
If the amplitude of the two possible paths is known, from quantum theory, the both amplitudes need to be summed and then the sum modulus has to be squared to obtain the intensity (interference between both wave functions). As in this experiment the electrons would behave like pure solid particles, there would be no interference between different possible wave functions so the intensity pattern is the sum of the separate modulus squared of the amplitude pattern.