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The concept that matter behaves like a wave was proposed by French physicist Louis de Broglie (/ d ə ˈ b r ɔɪ /) in 1924, and so matter waves are also known as de Broglie waves. The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h: =.
The de Broglie relation, [10] [11] [12] also known as de Broglie's momentum–wavelength relation, [4] generalizes the Planck relation to matter waves. Louis de Broglie argued that if particles had a wave nature, the relation E = hν would also apply to them, and postulated that particles would have a wavelength equal to λ = h / p .
In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle. This was confirmed by experiments soon afterward.
A photon of wavelength comes in from the left, collides with a target at rest, and a new photon of wavelength ′ emerges at an angle . The target recoils, and the photons have provided momentum to the target. where h is the Planck constant (6.626×10 −34 J⋅s).
The De Broglie relations give the relation between them: ... λ = wavelength of emitted photon, during electronic transition from E i to E j ...
On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. The critical temperature is the transition point between these two regimes, and at this ...
electron thermal de Broglie wavelength, approximate average de Broglie wavelength of electrons in a plasma: ...
Nowadays, this wavelength is called the de Broglie wavelength. For example, the electrons in a CRT display have a De Broglie wavelength of about 10 −13 m. To prevent the wave function for such a particle being spread over all space, de Broglie proposed using wave packets to represent particles that are localized in space. [25]