Scattering theory in the context of Hardy space


Scattering theory in the context of Hardy space

Scattering theory Study page number 1 of 1

Play TriviaQuestions Online!

or

Skip to study material about Scattering theory in the context of "Hardy space"


⭐ Core Definition: Scattering theory

In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of cathode rays (electron beams) and X-rays was observed and discussed. With the discovery of subatomic particles (e.g. Ernest Rutherford in 1911) and the development of quantum theory in the 20th century, the sense of the term became broader as it was recognized that the same mathematical frameworks used in light scattering could be applied to many other phenomena.

Scattering can refer to the consequences of particle-particle collisions between molecules, atoms, electrons, photons and other particles. Examples include: cosmic ray scattering in the Earth's upper atmosphere; particle collisions inside particle accelerators; electron scattering by gas atoms in fluorescent lamps; and neutron scattering inside nuclear reactors.

↓ Menu
HINT:

👉 Scattering theory in the context of Hardy space

In complex analysis, the Hardy spaces (or Hardy classes) are spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz (Riesz 1923), who named them after G. H. Hardy, because of the paper (Hardy 1915). In real analysis Hardy spaces are spaces of distributions on the real n-space , defined (in the sense of distributions) as boundary values of the holomorphic functions. Hardy spaces are related to the L spaces. For these Hardy spaces are subsets of spaces, while for the spaces have some undesirable properties, and the Hardy spaces are much better behaved. Hence, spaces can be considered extensions of spaces.

Hardy spaces have a number of applications, both in mathematical analysis itself as well as in interdisciplinary areas such as control theory (e.g. methods) and scattering theory.

↓ Explore More Topics
In this Dossier

Scattering theory in the context of Elastic scattering

Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the internal states of the particles involved stay the same. In the non-relativistic case, where the relative velocities of the particles are much less than the speed of light, elastic scattering simply means that the total kinetic energy of the system is conserved. At relativistic velocities, elastic scattering also requires the final state to have the same number of particles as the initial state and for them to be of the same kind.

View the full Wikipedia page for Elastic scattering
↑ Return to Menu

Scattering theory in the context of Atmospheric physics

Within the atmospheric sciences, atmospheric physics is the application of physics to the study of the atmosphere. Atmospheric physicists attempt to model Earth's atmosphere and the atmospheres of the other planets using fluid flow equations, radiation budget, and energy transfer processes in the atmosphere (as well as how these tie into boundary systems such as the oceans). In order to model weather systems, atmospheric physicists employ elements of scattering theory, wave propagation models, cloud physics, statistical mechanics and spatial statistics which are highly mathematical and related to physics. It has close links to meteorology and climatology and also covers the design and construction of instruments for studying the atmosphere and the interpretation of the data they provide, including remote sensing instruments. At the dawn of the space age and the introduction of sounding rockets, aeronomy became a subdiscipline concerning the upper layers of the atmosphere, where dissociation and ionization are important.

View the full Wikipedia page for Atmospheric physics
↑ Return to Menu

Scattering theory in the context of S-matrix

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).

More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states: a multi-particle state is said to be free (or non-interacting) if it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of one-particle states as prescribed by equation (1) below. Asymptotically free then means that the state has this appearance in either the distant past or the distant future.

View the full Wikipedia page for S-matrix
↑ Return to Menu