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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 : λ = h p . {\displaystyle \lambda ...
Louis de Broglie's early results on the pilot wave theory were presented in his thesis (1924) in the context of atomic orbitals where the waves are stationary.Early attempts to develop a general formulation for the dynamics of these guiding waves in terms of a relativistic wave equation were unsuccessful until in 1926 Schrödinger developed his non-relativistic wave equation.
The de Broglie–Bohm theory describes a pilot wave (,) in a configuration space and trajectories () of particles as in classical mechanics but defined by non-Newtonian mechanics. [5] At every moment of time there exists not only a wavefunction, but also a well-defined configuration of the whole universe (i.e., the system as defined by the ...
De Broglie proposed that the frequency f of a matter wave equals E/h, where E is the total energy of the particle and h is the Planck constant.For a particle at rest, the relativistic equation E=mc 2 allows the derivation of the Compton frequency f for a stationary massive particle, equal to mc 2 /h.
This animation portrays the de Broglie phase and group velocities (in slow motion) of three free electrons traveling over a field 0.4 ångströms in width. The momentum per unit mass (proper velocity) of the middle electron is lightspeed, so that its group velocity is 0.707 c. The top electron has twice the momentum, while the bottom electron ...
Louis Victor Pierre Raymond, 7th Duc de Broglie (/ d ə ˈ b r oʊ ɡ l i /, [1] also US: / d ə b r oʊ ˈ ɡ l iː, d ə ˈ b r ɔɪ /; [2] [3] French: [də bʁɔj] [4] [5] or [də bʁœj] ⓘ; 15 August 1892 – 19 March 1987) [6] was a French theoretical physicist and aristocrat known for his contributions to quantum theory.
The notion of group velocity is based on a linear approximation to the dispersion relation () near a particular value of . [6] In this approximation, the amplitude of the wave packet moves at a velocity equal to the group velocity without changing shape. This result is an approximation that fails to capture certain interesting aspects of the ...
Using the de Broglie relations for energy and momentum for matter waves, E = ℏ ω , p = ℏ k , {\displaystyle E=\hbar \omega \,,\quad \mathbf {p} =\hbar \mathbf {k} \,,} where ω is the angular frequency and k is the wavevector with magnitude | k | = k , equal to the wave number , the energy–momentum relation can be expressed in terms of ...