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In physics, particularly in quantum perturbation theory, the matrix element refers to the linear operator of a modified Hamiltonian using Dirac notation.It is in fact referring to the matrix elements of a Hamiltonian operator which serves the purpose of calculating transition probabilities between different quantum states.
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics.
The idea of automation of the calculations in high-energy physics is not new. It dates back to the 1960s when packages such as SCHOONSCHIP and then REDUCE had been developed. These are symbolic manipulation codes that automatize the algebraic parts of a matrix element evaluation, like traces on Dirac matrices and contraction of Lorentz indices.
Matrix element may refer to: The (scalar) entries of a matrix. Matrix element (physics), the value of a linear operator (especially a modified Hamiltonian) in quantum theory; Matrix coefficient, a type of function in representation theory; Element (software), free and open-source software instant messaging client implementing the Matrix protocol
In quantum physics, Fermi's golden rule is a formula that describes the transition rate ... The phase of this matrix element, however, contains separate information ...
In theoretical physics, the matrix theory is a quantum mechanical model proposed in 1997 by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind; it is also known as BFSS matrix model, after the authors' initials.
In elementary particle physics and mathematical physics, in particular in effective field theory, a form factor is a function that encapsulates the properties of a certain particle interaction without including all of the underlying physics, but instead, providing the momentum dependence of suitable matrix elements.
The initial elements of S-matrix theory are found in Paul Dirac's 1927 paper "Über die Quantenmechanik der Stoßvorgänge". [1] [2] The S-matrix was first properly introduced by John Archibald Wheeler in the 1937 paper "On the Mathematical Description of Light Nuclei by the Method of Resonating Group Structure". [3]