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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 ...
The de Broglie–Bohm theory describes the physics in the Bell test experiments as follows: to understand the evolution of the particles, we need to set up a wave equation for both particles; the orientation of the apparatus affects the wavefunction.
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 wave-like behaviour of particles discovered by de Broglie was used by Erwin Schrödinger in his formulation of wave mechanics. [ 7 ] : 270 De Broglie's pilot-wave concept, [ 8 ] was presented at the 1927 Solvay Conferences then abandoned, in favor of the quantum mechanics , until 1952 when it was rediscovered and enhanced by David Bohm .
The equation says the matter wave frequency in vacuum varies with wavenumber (= /) in the non-relativistic approximation. The variation has two parts: a constant part due to the de Broglie frequency of the rest mass ( ℏ ω 0 = m 0 c 2 {\displaystyle \hbar \omega _{0}=m_{0}c^{2}} ) and a quadratic part due to kinetic energy.
Planck–Einstein equation and de Broglie wavelength relations P = (E/c, p) is the four-momentum, ... List of equations in wave theory; List of photonics equations;
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
De Broglie also arrived at the same equation in 1928. This relativistic wave equation is now most commonly known as the Klein–Gordon equation. [21] In 1927, Pauli phenomenologically found a non-relativistic equation to describe spin-1/2 particles in electromagnetic fields, now called the Pauli equation. [22]