Collision between Two Particles

V. A. Sidorovich

Nelson Enrique Bolivar, Gabriel Abellán

The theory of scattering consists in studying the collision also called dispersion, between two or more particles. This chapter studies the simplest case of the collision between two particles without spin. Historically, the discovery of the quantum world and the particles was made by studying collision processes. Many physics experiments are based on collisions, or more precisely of scattering. In 2012 particle physicists announced the long awaited discovery of the Higgs Boson in the collision processes at the Large Hadron Collider (LHC). An incoming spherical wave does not correspond to an usual experimental situation. In an experimental situation, the incoming wave is more often modeled by an incident plane wave.

Okuyama Kikuo, Hiroaki Masuda, Ko Higashitani +2 more

James Chadwick

Abstract The problem of the collision of two particles which act upon each other with forces varying as the inverse square of the distance between them has been solved exactly on the basis of the new quantum mechanics, and the solution is the same as that given by classical mechanics. In a recent paper, however, Mott has pointed out that this agreement between the predictions of classical mechanics and wave mechanics depends upon the dissimilarity of the colliding particles; if the particles are identical the scattering laws given by the wave mechanics will be very different from those of classical theory. Mott has considered the two types of collision between similar particles, (1) in which the particles possess spin, such as the collisions of electrons with electrons or protons with hydrogen nuclei, and (2) in which the particles have no spin, such as the collisions of α-particles with helium nuclei.

Walter Hahn, Boris V. Fine

We consider multiple collisions of quantum wave packets in one dimension. The system under investigation consists of an impenetrable wall and two hard-core particles with very different masses. The lighter particle bounces between the heavier one and the wall. Both particles are initially represented by narrow Gaussian wave packets. A complete analytical solution of this problem is presented. The idea of the method used is to decompose the two-particle wave function into a continuous superposition of terms (channels), such that the multiple collisions within each channel do not lead to subsequent entanglement between the two particles. For each channel, the time evolution of the two-particle wave function is completely determined by the motion of the corresponding classical pointlike particles; therefore the whole quantum problem is reduced to a classical calculation. The calculation based on the above method reveals the following unexpected result: The entanglement between the two particles first increases with time due to the collisions, but then it begins to decrease, disappearing completely when the light particle becomes too slow to catch up with the heavy one.