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In mathematical physics, scattering theory is a framework for studying and understanding the interaction or scattering of solutions to partial differential equations. In acoustics , the differential equation is the wave equation , and scattering studies how its solutions, the sound waves , scatter from solid objects or propagate through non ...
It relates the scattered wave function with the interaction that produces the scattering (the scattering potential) and therefore allows calculation of the relevant experimental parameters (scattering amplitude and cross sections). The most fundamental equation to describe any quantum phenomenon, including scattering, is the Schrödinger equation.
The following description follows the canonical way of introducing elementary scattering theory. A steady beam of particles scatters off a spherically symmetric potential V ( r ) {\displaystyle V(r)} , which is short-ranged, so that for large distances r → ∞ {\displaystyle r\to \infty } , the particles behave like free particles.
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics , scattering theory and quantum field theory (QFT).
Individual particle physics events are modeled by scattering theory based on an underlying quantum field theory of the particles and their interactions. The S-matrix is used to characterize the probability of various event outgoing particle states given the incoming particle states.
Multiple-scattering effects of light scattering by particles are treated by radiative transfer techniques (see, e.g. atmospheric radiative transfer codes). The relative size of a scattering particle is defined by its size parameter x, which is the ratio of its characteristic dimension to its wavelength:
The physical phenomenon was explained by Rutherford in a classic 1911 paper [1] that eventually led to the widespread use of scattering in particle physics to study subatomic matter. Rutherford scattering or Coulomb scattering is the elastic scattering of charged particles by the Coulomb interaction.
Thomson scattering is a model for the effect of electromagnetic fields on electrons when the field energy is much less than the rest mass of the electron .In the model the electric field of the incident wave accelerates the charged particle, causing it, in turn, to emit radiation at the same frequency as the incident wave, and thus the wave is scattered.