Transmission coefficient
The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered.
All the meanings are very similar in concept: In chemistry, the transmission coefficient refers to a chemical reaction overcoming a potential barrier; in optics and telecommunications it is the amplitude of a wave transmitted through a medium or conductor to that of the incident wave; in quantum mechanics it is used to describe the behavior of waves incident on a barrier, in a way similar to optics and telecommunications.
Although conceptually the same, the details in each field differ, and in some cases the terms are not an exact analogy.
In chemistry, in particular in transition state theory, there appears a certain "transmission coefficient" for overcoming a potential barrier.
The transmission coefficient is a measure of how much of an electromagnetic wave (light) passes through a surface or an optical element.
Transmission coefficients can be calculated for either the amplitude or the intensity of the wave.
[1] Consider a wave travelling through a transmission line with a step in impedance from
is uniquely determined from first principles by noting that the incident power on the discontinuity must equal the sum of the power in the reflected and transmitted waves: Solving the quadratic for
[1] The value of the transmission coefficient is inversely related to the quality of the line, circuit, channel or trunk.
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: where
is the probability current in the wave incident upon the barrier with normal unit vector
is the probability current in the wave moving away from the barrier on the other side.
The reflection coefficient R is defined analogously: Law of total probability requires that
[2][failed verification] In the classical limit of all other physical parameters much larger than the reduced Planck constant, denoted
This classical limit would have failed in the situation of a square potential.
