# Guide Scattering Theory Contents:

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When two atoms are scattered off one another, one can understand them as being the bound state solutions of some differential equation. The scattering of two hydrogen atoms will disturb the state of each atom, resulting in one or both becoming excited, or even ionized , representing an inelastic scattering process.

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The term " deep inelastic scattering " refers to a special kind of scattering experiment in particle physics. In mathematics , scattering theory deals with a more abstract formulation of the same set of concepts. For example, if a differential equation is known to have some simple, localized solutions, and the solutions are a function of a single parameter, that parameter can take the conceptual role of time. One then asks what might happen if two such solutions are set up far away from each other, in the "distant past", and are made to move towards each other, interact under the constraint of the differential equation and then move apart in the "future".

The scattering matrix then pairs solutions in the "distant past" to those in the "distant future". Solutions to differential equations are often posed on manifolds. Frequently, the means to the solution requires the study of the spectrum of an operator on the manifold.

## Scattering Theory - 1st Edition

As a result, the solutions often have a spectrum that can be identified with a Hilbert space , and scattering is described by a certain map, the S matrix , on Hilbert spaces. Spaces with a discrete spectrum correspond to bound states in quantum mechanics, while a continuous spectrum is associated with scattering states. The study of inelastic scattering then asks how discrete and continuous spectra are mixed together. An important, notable development is the inverse scattering transform , central to the solution of many exactly solvable models.

Advanced topics. Quantum annealing Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum gravity Quantum information science Quantum machine learning Perturbation theory quantum mechanics Relativistic quantum mechanics Scattering theory Spontaneous parametric down-conversion Quantum statistical mechanics.

Backscattering Brillouin scattering Compton scattering Diffuse sky radiation Extinction Haag—Ruelle scattering theory Linewidth Mie theory Molecular scattering Raman scattering Rayleigh scattering S-matrix Scattering from rough surfaces Scintillation physics. Quantum mechanics. Introduction History timeline Glossary Classical mechanics Old quantum theory. Q-analog List Quantum algebra Quantum calculus Quantum differential calculus Quantum geometry Quantum group Quantum Bayesianism Quantum biology Quantum chemistry Quantum chaos Quantum cognition Quantum cosmology Quantum dynamics Quantum economics Quantum evolution Quantum finance Quantum game theory Quantum measurement problem Quantum mind Quantum probability Quantum social science Quantum stochastic calculus Quantum spacetime.

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Quantum statistical mechanics Relativistic quantum mechanics Quantum field theory Axiomatic quantum field theory Quantum field theory in curved spacetime Thermal quantum field theory Topological quantum field theory Local quantum field theory Conformal field theory Two-dimensional conformal field theory Liouville field theory History Quantum gravity. Categories : Scattering theory Scattering, absorption and radiative transfer optics Quantum mechanics Hilbert space.

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