Miguel Almagro
At the close of the 19th century, the case for atomic theory , that matter was made of particulate objects or atoms , was well established. Electricity, first thought to be a fluid, was now understood to consist of particles called electrons , as demonstrated by J.J. Thomson by his research into the work of Ernest Rutherford , who had investigated using cathode rays that an electrical charge would actually travel across a vacuum from cathode to anode. In brief, it was understood that much of nature was made of particles. At the same time, waves were well understood, together with wave phenomena such as diffraction and interference . Light was believed to be a wave, as Thomas Young's double-slit experiment and effects such as Fraunhofer diffraction had clearly demonstrated the wave-like nature of light.
But as the 20th century turned, problems had emerged. Albert Einstein 's analysis of the photoelectric effect in 1905 demonstrated that light also possessed particle-like properties, and this was further confirmed with the discovery of the Compton effect in 1923. Later on, the diffraction of electrons would be predicted and experimentally confirmed, thus showing that electrons must have wave-like properties in addition to particle properties.
This confusion over particle versus wave properties was eventually resolved with the advent and establishment of quantum mechanics in the first half of the 20th century, which ultimately explained wave–particle duality . It provided a single unified theoretical framework for understanding that all matter may have characteristics associated with particles and waves. Quantum mechanics holds that every particle in nature, be it a photon ,electron or atom , is described by a solution to a differential equation , most typically, the Schrödinger equation . The solutions to this equation are known as wave functions , as they are inherently wave-like in their form. They can diffract and interfere , leading to the wave-like phenomena that are observed. Yet also, the wave functions are interpreted as describing the probability of finding a particle at a given point in space. Thus, if one is looking for a particle, one will find one with a probability density given by the square of the magnitude of the wave function.
One does not observe the wave-like quality of everyday objects because the associated wavelengths are exceedingly small.