Reality → Energy → Particles → Wave-particle duality
Depending on the experiment, particles may either show their particle or their wave nature. The paradoxical duality has been raised to a fundamental principle of quantum mechanics through the work of Bohr, de Broglie, Einstein, Heisenberg, Schrödinger and other great minds. The wave nature of light shows clearly in such phenomena as interference, diffraction, and polarization and is also strongly supported by Maxwell’s equations. Waves can however not explain the photoelectric effect, where the energy of the released electrons does not depend on light’s intensity but rather on its frequency, a phenomenon explained by the particle nature of photons. Another demonstration of the particle nature of electromagnetic radiation is the Compton effect, which can be observed in the scattering of X-rays on crystals (photons bounce off electrons in a process resembling the elastic collision of two unequal balls). De Broglie broadened the duality concept by postulating that not only photons but also electrons [1] and all other matter particles possess wave nature. Phenomena such as interference and diffraction have subsequently been observed in experiments with protons, neutrons, atoms, and even some molecules (momentum grows exponentially with the size of composite particles and the wavelength becomes undetectably small for larger molecules). Schrödinger developed a mathematical equation that combines the wave and particle phenomena; Dirac expanded the equation to include particle movements at velocities comparable to the speed of light. The uncertainty principle, formulated by Heisenberg, provides an important link between wave and particle properties.
Scattering of electrons on a polished nickel crystal surface ( Davisson–Germer experiment) produced interference patterns as known from electromagnetic radiation and thereby provided the first evidence confirming de Broglie's hypothesis.