Particle-Wave Duality

Around the year 1700, Isaac Newton suggested that light was made up of particles, which he called, “corpuscles”. At the same time, Christiaan Huygens opposed Newton, arguing that light was a wave since the corpuscular theory could not explain diffraction and interference phenomena, discovered by Francesco Maria Grimaldi in 1665. A century later, Augustin-Jean Fresnel established a mathematical theory of light interference. He devised the physical laws of reflection and refraction in 1815. Two years later, in 1817, Thomas Young calculated the wavelength of light from an interference pattern, providing stronger foundations for the wavelike nature of light. In 1864, James Clerk Maxwell predicted the existence of electromagnetic waves, of which light comprised a very small part of. In 1861, he presented his four equations for electromagnetic theory showing that the magnetic field produced by a magnet and the electric field generated between two parallel metal plates connected to a charged capacitor were inextricably linked to one another. This led to the introduction of the concept of electromagnetic waves other than visible light.

Maxwells Eqns

On the other hand, the wave theory could not explain the photoelectric effect, discovered by Hertz in 1887. With both theories conflicting one another, it later turned out that both were correct. Light can sometimes behave as a particle and sometimes as a wave. This theory is now called “wave-particle duality”.

In 1924, De Broglie, greatly influenced by Einstein, wrote in his doctoral thesis, that the wave-particle duality should be associated with not only light, but to the physical world too. He suggested that, the propagation of a wave is associated with the motion of a particle; photon, atom, electron, proton, etc.

“Nature loves symmetry. Light is dualistic in nature, behaving in some situations like particles and in others like waves. If nature is symmetric, this duality should also hold for matter. Electrons and protons which we usually think of as particles, may in some situations behave likes waves”. – De Broglie

De Broglie proposed that a particle has associated with it, a wave, which in essence could be visualised as a pulse of energy or wave packet, and therefore has a frequency and wavelength. The probability of finding a particle at a particular location in space is related to its wave function. The larger the amplitude of the wave function at a particular point, the greater the probability that the particle will be found there. The pulse has two velocities associated with it, the phase velocity and the group velocity of the wave packet. The wave packet is spread over a point in space. De Broglie identified the group velocity as the velocity of the particle which has assigned to it, particular properties such as momentum:


in exactly the same way as for a photon


If the particles speed approaches the speed of light, then


De Broglie’s wave hypothesis was confirmed in 1927 by the Davisson-Germer experiment, the first direct evidence for the particle wave nature of matter. In their experiment they fired a beam of electrons on to a crystal. By doing so, they observed a diffraction, indicative of a wave like nature of the electrons.


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