# A Guide to Wave Particle Duality in Electron Diffraction

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Before the development of quantum mechanics, Einstein showed that the light, which had been considered as electromagnetic wave, exhibit properties of particles and must considered as particle like.

Although, de Broglie proposed that the particles can be also considered as wave-like and the Davisson-Germer experiment confirmed the de Broglie’s hypothesis. In 1928 Bohr introduced the complementarity principle which states that the complete knowledge of phenomena in quantum mechanics requires the description of both wave and particle properties. For this reason wave-particle duality enlighten deep understanding of atomic and subatomic scale.

## Wave-Particle Duality

Young’s double-slit experiment is a well known experiment in quantum mechanics which is the demonstration of interference of light. According to this, Young found that when a point source of light illuminates the two slits in a screen, image of light on second screen is diffraction pattern. With the help of this experiment, Young obtained an important result that light is a wave. However, in 1927 David and Germer later by Thomson demonstrated double-slit experiment by the making use of electrons and show that electrons also show same behavior. On the other hand, according to classical physics, waves exhibit interference, particles do not. Consequently, in the quantum scale all particles exhibit wave-particle nature and this phenomena cannot be explained by the classical wave or particle assumptions.

Therefore, in 1926 Bohr and his followers laid out the groundwork for quantum mechanics using results of David-Germer’s double-slits experiments. This view is known as Copenhagen interpolation and aimed to explain probabilistic nature of quantum mechanics. According to this, the behavior of electron can be explained as follows:

• Electron is represented by wave packet and interference or wave phenomenon occurs when the wavelength of wave packet equals to distance between splits. Therefore when de Broglie of wavelength of an object exceeds its size, the wave property of object is detectable
• If we define wave function Ψ(x,t) to characterize wave packet, this function represents all electrons from same source. Thus, wave function provide us to calculate of probability of finding an electron at any point of space.
• Electron exhibits wave properties while passes through the double splits but it interacts like a particle with the second screen. According to this, wave and particle character are complementary, it is not possible to observe both wave and particle properties simultaneously. This is also known as complementary principle which is introduced by Niels Bohr.
• Electron does not go through from source to screen in certain path. According to observability principle, a quantity cannot be defined unless it has been observed.
• When a measurement is made to detect an electron, energy and position of electron is disturbed by the measurement. As a result, physics in microscopic scale is non deterministic unlike the classical physics.

As a result, David-Germer’s experiment demonstrates the role of observer in the quantum realm and seems to be also the milestone for the quantum mechanics. However, results of experiment has inspired Heisenberg to postulate uncertainty which states that it is impossible to design an apparatus which allows us to determine the slit that the electron went through without disturbing the electron enough to destroy the interference pattern.’. Consequently, wave and particle property of quantum entity cannot be handled independently.

## Sources

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Written by

### Kazim Gokhan Atman

Kazim Gokhan Atman is a Ph.D. student in mathematical physics. He is mainly focused on fractional calculus and possible violation of locality at a small distance in Quantum Field Theory.

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