# de Broglie hypothesis

Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter can exhibit wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. The concept that matter behaves like a wave was proposed by Louis de Broglie in 1924. It is also referred to as the *de Broglie hypothesis* Matter waves are referred to as de Broglie waves. Any aspect of the behaviour or properties of a material object that varies in time or space in conformity with the mathematical equations that describe waves. The de Broglie matter wave would be a stationary wave, which only allows for some very specific modes of vibration (quantization) that would be n entire wavelengths.

The de Broglie wavelength is the wavelength, λ, associated with a massive particle and is related to its momentum, p, through the Planck constant, h:

**λ = h/p = h/(mv)
**

where *m* is the mass of the particle and *v* is its velocity.

De Broglie waves account for the appearance of subatomic particles at conventionally unexpected sites because their waves penetrate barriers much as sound passes through walls. Thus a heavy atomic nucleus occasionally can eject a piece of itself in a process called alpha decay. The piece of nucleus (alpha particle) has insufficient energy as a particle to overcome the force barrier surrounding the nucleus; but as a wave it can leak through the barrier—that is, it has a finite probability of being found outside the nucleus.

De Broglie waves around a closed loop, such as would be associated with electrons circling nuclei in atoms, can persist only if the standing waves fit evenly around the loop; otherwise they cancel themselves out. This requirement causes the electrons in atoms to select only particular configurations, or states, among the many that would otherwise be available.

de Broglie’s hypothesis: wave-particle duality

Quantum Wave Interference simulation

REFERENCES

Encyclopædia Britannica. Available in: https://www.britannica.com/science/de-Broglie-wave. Access in: 05/09/2018.

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