# de Broglie relation

## de Broglie relation

[də¦brȯ¦glē ri′lā·shən]
(quantum mechanics)
The relation in which the de Broglie wave associated with a free particle of matter, and the electromagnetic wave in a vacuum associated with a photon, has a wavelength equal to Planck's constant divided by the particle's momentum and a frequency equal to the particle's energy divided by Planck's constant. Also known as de Broglie equation.
References in periodicals archive ?
The wave mechanics shows that the momentum 3-vector of an electron of a rest mass [m.sub.0] (in vacuum) is given by the de Broglie relation
In quantum mechanics, momentum of microparticles p=mv, where m and v are respectively, the rest mass and the speed of the microparticles, with its wavelength [lambda] associated by de Broglie relation (p=h/[lambda]) [4].
The force difference [DELTA][F.sub.4] = 0 gives the de Broglie relation
The expression m[upsilon][lambda] = h used in (1) to arrive at the total electron kinetic energy is the de Broglie relation expressed in simple, physically intuitive terms: the de Broglie relation yields the product of the electron mass m, its average velocity [upsilon], and the path length [lambda] over which its instantaneous velocity varies.
Thus Beckmann's de Broglie relation is in relativistic agreement with the PV result.
The equation [DELTA][F.sub.3] = 0 from the final two brackets yields the de Broglie relation
567], in order to apply the de Broglie relation, the following assumption is made
From this equation the momentum of the electron is calculated as [absolute value of p] = [??]/c, and from the de Broglie relation it follows that [lambda] = hc/[??].
associates a Compton wavelength [[lambda].sub.c](or a Compton radius [r.sub.c] = [[lambda].sub.c]/2[pi]) with the particle mass m, while the de Broglie relation [3, p.81]
The de Broglie relations derived from the electron and proton coupling to the Planck vacuum state.
This phase wave in terms of transmitting the particle mass at the speed v and angular frequency [[OMEGA].sub.d] = 2[pi]v/[[LAMBDA].sub.d], with [[LAMBDA].sub.d] and [[OMEGA].sub.d] obeying the de Broglie relations, represents a de Broglie wave.
The solutions for a basic material particle generally in motion, with the charge quantity (accompanied with a spin) and energy of the charge as the sole inputs, predict accurately the inertial mass, total wave function, total energy equal to the mass times [c.sup.2], total momentum, kinetic energy and linear momentum of the particle, and that the particle is a de Broglie wave, it obeys Newton's laws of motion, de Broglie relations, Schrodinger equation in small geometries, Newton's law of gravitation, and Galilean-Lorentz-Einstein transformation at high velocities.

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