Classical physics predicts that light behaves like a wave; the diffraction and interference effects of optics come from the wave nature of light. However, by 1905, Max Planck and Albert Einstein had established that light also acts like a particle; by specifying that light energy comes in packets called photons, the classical inability to explain effects such as blackbody radiation spectra and the photoelectric effect had been resolved. Therefore, the nature of photons is somewhat ambiguous; depending on how you observe them, they sometimes behave as particles, and sometimes as waves.

In his 1924 doctoral dissertation, Louis de Broglie speculated that matter might also have this dual particle-wave nature. For the frequency and wavelength of the matter waves, he chose the same relations that hold for light: f = E/h and (lambda) = h/p, where h is Plancküs constant. This idea was pure speculation at first, but...