Conservation of momentum in the context of Frame of reference

The electron neutrino (ν
_e) is an elementary particle which has zero electric charge and a spin of 1⁄2. Together with the electron, it forms the first generation of leptons, hence the name electron neutrino. It was first hypothesized by Wolfgang Pauli in 1930, to account for missing momentum and missing energy in beta decay, and was discovered in 1956 by a team led by Clyde Cowan and Frederick Reines (see Cowan–Reines neutrino experiment).

In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons. The total energy and momentum of the initial pair are conserved in the process and distributed among a set of other particles in the final state. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of such an original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy, conservation of momentum, and conservation of spin are obeyed.

During a low-energy annihilation, photon production is favored, since these particles have no mass. High-energy particle colliders produce annihilations where a wide variety of exotic heavy particles are created.

Recoil (often called knockback, kickback or simply kick) is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, for according to Newton's third law the force required to accelerate something will evoke an equal but opposite reactional force, which means the forward momentum gained by the projectile and exhaust gases (ejectae) will be mathematically balanced out by an equal and opposite impulse exerted back upon the gun.

In crystallography and solid state physics, the Laue equations relate incoming waves to outgoing waves in the process of elastic scattering, where the photon energy or light temporal frequency does not change upon scattering by a crystal lattice. They are named after physicist Max von Laue (1879–1960).

The Laue equations can be written as ${\displaystyle \mathbf {\Delta k} =\mathbf {k} _{\mathrm {out} }-\mathbf {k} _{\mathrm {in} }=\mathbf {G} }$ as the condition of elastic wave scattering by a crystal lattice, where ${\displaystyle \mathbf {\Delta k} }$ is the scattering vector, ${\displaystyle \mathbf {k} _{\mathrm {in} }}$, ${\displaystyle \mathbf {k} _{\mathrm {out} }}$ are incoming and outgoing wave vectors (to the crystal and from the crystal, by scattering), and ${\displaystyle \mathbf {G} }$ is a crystal reciprocal lattice vector. Due to elastic scattering ${\displaystyle |\mathbf {k} _{\mathrm {out} }|^{2}=|\mathbf {k} _{\mathrm {in} }|^{2}}$, three vectors. ${\displaystyle \mathbf {G} }$, ${\displaystyle \mathbf {k} _{\mathrm {out} }}$, and ${\displaystyle -\mathbf {k} _{\mathrm {in} }}$ , form a rhombus if the equation is satisfied. If the scattering satisfies this equation, all the crystal lattice points scatter the incoming wave toward the scattering direction (the direction along ${\displaystyle \mathbf {k} _{\mathrm {out} }}$). If the equation is not satisfied, then for any scattering direction, only some lattice points scatter the incoming wave. (This physical interpretation of the equation is based on the assumption that scattering at a lattice point is made in a way that the scattering wave and the incoming wave have the same phase at the point.) It also can be seen as the conservation of momentum as ${\displaystyle \hbar \mathbf {k} _{\mathrm {out} }=\hbar \mathbf {k} _{\mathrm {in} }+\hbar \mathbf {G} }$ since ${\displaystyle \mathbf {G} }$ is the wave vector for a plane wave associated with parallel crystal lattice planes. (Wavefronts of the plane wave are coincident with these lattice planes.)