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The transmission coefficient represents the probability flux of the transmitted wave relative to that of the incident wave. This coefficient is often used to describe the probability of a particle tunneling through a barrier. The transmission coefficient is defined in terms of the incident and transmitted probability current density J according to:
But in computing the power transmission (below), these factors must be taken into account. The simplest way to obtain the power transmission coefficient (transmissivity, the ratio of transmitted power to incident power in the direction normal to the interface, i.e. the y direction) is to use R + T = 1 (conservation of energy). In this way we find
The general form of the Eyring–Polanyi equation somewhat resembles the Arrhenius equation: = ‡ where is the rate constant, ‡ is the Gibbs energy of activation, is the transmission coefficient, is the Boltzmann constant, is the temperature, and is the Planck constant.
Thinfilm is a web interface that implements the transfer-matrix method, outputting reflection and transmission coefficients, and also ellipsometric parameters Psi and Delta. Luxpop.com is another web interface that implements the transfer-matrix method. Transfer-matrix calculating programs in Python and in Mathematica.
In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively T and R; they measure the extent the particles reflect from the potential barrier or are transmitted through it.
For the case of 1/2 fermions, like electrons and neutrinos, the solutions of the Dirac equation for high energy barriers produce transmission and reflection coefficients that are not bounded. This phenomenon is known as the Klein paradox.
The primary coefficients are the physical properties of the line, namely R,C,L and G, from which the secondary coefficients may be derived using the telegrapher's equation. In the field of transmission lines, the term transmission coefficient has a different meaning despite the similarity of name: it is the companion of the reflection coefficient.
From the equations, the power series must start with at least an order of to satisfy the real part of the equation; for a good classical limit starting with the highest power of the Planck constant possible is preferable, which leads to = = and = = (), with the following constraints on the lowest order terms, () = (()) and () =