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Encyclopedia > Scattering channel

In scattering theory, a scattering channel is a quantum state of the colliding system before or after the collision (t to pm infty). The Hilbert space spanned by the states before collision (in states) is equal to the ones spanned by the states after collision (out states) which are both Fock spaces if there is a mass gap. This is the reason why the S matrix which maps the in states onto the out states must be unitary. The scattering channel are also called scattering asymptotes. The Møller operators are mapping the scattering channels onto the corresponding states which are solution of the Schrödinger equation taking the interaction Hamiltonian into account. The Møller operators are isometric. Scattering theory is a branch of physics and especially of quantum mechanics whose aim is the study of scattering events. ... A quantum state is any possible state in which a quantum mechanical system can be. ... In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. ... The Fock space is an algebraic system (Hilbert space) used in quantum mechanics to describe quantum states with a variable or unknown number of identical particles. ... A quantum field theory model is said to have a mass gap if the energy spectrum not including zero has a positive greatest lower bound. ... The S-matrix is the matrix in quantum mechanics or quantum field theory that relates the final state in the infinite future and the initial state in the infinite past. ... In functional analysis, a unitary operator is a bounded linear operator U on a Hilbert space satisfying U*U=UU*=I where I is the identity operator. ... An asymptote is a straight or curved line which a curve will approach arbitrarily closely. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ... Interaction is a kind of action which occurs as two or more objects have an effect upon one another. ... The Hamiltonian, denoted H, has two distinct but closely related meanings. ... In mathematics, an isometry, isometric isomorphism or congruence mapping is a distance-preserving isomorphism between metric spaces. ...

See also: LSZ formalism

  Results from FactBites:
 
Channel - Wikipedia, the free encyclopedia (194 words)
Channel (geography), the course traveled by a body of water between land masses
Ion channel, a channel in a plasma membrane which helps certain ions to enter/exit a biological cell
Scattering channel, in scattering theory, a possible state of the colliding system
SSC:IRAC: Scattered and stray light (1065 words)
Scattered light is well-rejected by the post-BCD pipeline if dithering and mapping offsets are large enough to ensure stars are moved out of the scattering zones, and the redundancy is high enough to allow for effective outlier rejection.
In channels 1 and 2, the pattern is in the form of a "butterfly wing" at the bottom of the array in raw data coordinates (i.e., at the top of the array in BCD coordinates).
The origin of the scattered light is currently not known for sure, but the in-focus nature of the scattered light spots suggests that little or none is contributed by the telescope, and most arises within the MIC.
  More results at FactBites »


 

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