Transmission Coefficient

Electromagnetism

$T=\frac{I_T}{I_I}={\left(\frac{E_{0_T}}{E_{0_I}}\right)}^2$

Quantum Mechanics

$T={\left(1+\frac{{\sinh }^2(k_{\text{below}}a)}{4\eta (1-\eta )}\right)}^{-1},E<V_0$

• Probability that a particle will reflect off of a potential barrier for a finite square well
• $E$ is the kinetic energy of the particle
• $V_0$ is the potential energy of the barrier
• $\sinh$ is one of the hyperbolic trig functions
• $\eta =\frac{E}{V_0}$
• $k_{\text{below}}=\frac{\sqrt{2m{V}_0(1-\eta )}}{\hslash }$, where $\hslash$ is the reduced Planck constant in $4.135\cdot 10^{-15}\mathrm{eV}\cdot \mathrm{s}$, $m$ is given in $\frac{\mathrm{eV}}{{\mathrm{c}}^2}$. $m_e=0.51\frac{\mathrm{MeV}}{{\mathrm{c}}^2}=0.0017eV\cdot {\left(\frac{s}{m}\right)}^2$
• Based on Professor Dave Explains Video Pt. 2
• Desmos Demo

$T={\left(1+\frac{{\sin }^2(k_{\text{below}}a)}{4\eta (\eta -1)}\right)}^{-1},E>V_0$

• $k_{\text{below}}=\frac{\sqrt{2m{V}_0(\eta -1)}}{\hslash }$
• Desmos Demo