Quantum Mechanics in a Nutshell

Time: end of the 19th century. Maxwell’s equations have established Faraday’s hunch that light is an electromagnetic wave. However, by early 20th century, experimental evidence mounted pointing towards the fact that light is carried by ‘particles’ that pack a definite momentum and energy. Here is the crux of the problem: consider the double-slit experiment. Monochromatic light of wavelength passing through two slits separated by a distance d ⇠ forms a di↵raction pattern on a photographic plate. If one tunes down the intensity of light in a double-slit experiment, one does not get a ‘dimmer’ interference pattern, but discrete strikes on the photographic plate and illumination at specific points. That means light is composed of ‘particles’ whose energy and momentum are concentrated in one point which leads to discrete hits. But their wavelength extends over space, which leads to di↵raction patterns.