Search results
Results from the WOW.Com Content Network
In the de Broglie hypothesis, the velocity of a particle equals the group velocity of the matter wave. [ 2 ] : 214 In isotropic media or a vacuum the group velocity of a wave is defined by: v g = ∂ ω ( k ) ∂ k {\displaystyle \mathbf {v_{g}} ={\frac {\partial \omega (\mathbf {k} )}{\partial \mathbf {k} }}} The relationship between the ...
Particle velocity (denoted v or SVL) is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s). In many cases this is a longitudinal wave of pressure as with sound , but it can also be a transverse wave as with the vibration of a taut string.
where E is the energy of the wave, ħ is the reduced Planck constant, and c is the speed of light in a vacuum. For the special case of a matter wave, for example an electron wave, in the non-relativistic approximation (in the case of a free particle, that is, the particle has no potential energy):
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.
The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality.
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
If the wave function propagates according to the curved Dirac equation, then the particle moves according to the Mathisson-Papapetrou equations of motion, which are an extension of the geodesic equation. This relativistic wave-particle duality follows from the conservation laws for the spin tensor and energy-momentum tensor, [45] and also from ...
In physics, the acoustic wave equation is a second-order partial differential equation that governs the propagation of acoustic waves through a material medium resp. a standing wavefield. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position x and time t. A simplified (scalar) form of the ...