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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.
The Scattering transfer parameters or T-parameters of a 2-port network are expressed by the T-parameter matrix and are closely related to the corresponding S-parameter matrix. However, unlike S parameters, there is no simple physical means to measure the T parameters in a system, sometimes referred to as Youla waves.
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.
In one-dimensional quantum systems, is the scattering matrix and if it satisfies the Yang–Baxter equation then the system is integrable. The Yang–Baxter equation also shows up when discussing knot theory and the braid groups where R {\displaystyle R} corresponds to swapping two strands.
In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. [1] At large distances from the centrally symmetric scattering center, the plane wave is described by the wavefunction [ 2 ]
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 .
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.
The Transition Matrix Method (T-matrix method, TMM) is a computational technique of light scattering by nonspherical particles originally formulated by Peter C. Waterman (1928–2012) in 1965. [ 1 ] [ 2 ] The technique is also known as null field method and extended boundary condition method (EBCM). [ 3 ]