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The S-matrix is closely related to the transition probability amplitude in quantum mechanics and to cross sections of various interactions; the elements (individual numerical entries) in the S-matrix are known as scattering amplitudes. Poles of the S-matrix in the complex-energy plane are identified with bound states, virtual states or resonances.
Scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance (sunlight) scattered by rain drops to form a rainbow.
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 goal of the multistate Landau–Zener theory is to determine elements of the scattering matrix and the transition probabilities between states of this model after evolution with such a Hamiltonian from negative infinite to positive infinite time. The transition probabilities are the absolute value squared of scattering matrix elements.
Differential and total scattering cross sections are among the most important measurable quantities in nuclear, atomic, and particle physics. With light scattering off of a particle, the cross section specifies the amount of optical power scattered from light of a given irradiance (power per area). Although the cross section has the same units ...
In computational electromagnetics, the scattering-matrix method (SMM) is a numerical method used to solve Maxwell's equations, [1] related to the transfer-matrix method.
For monochromatic incident waves the self-consistent solution for the oscillating dipole moments may be found; from these the absorption and scattering cross sections are computed. If DDA solutions are obtained for two independent polarizations of the incident wave, then the complete amplitude scattering matrix can be determined.
S-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics. It avoided the notion of space and time by replacing it with abstract mathematical properties of the S -matrix .