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- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/06%3A_Appendices/6.02%3A_B-_The_Transfer_Matrix_MethodHence, ik−[ψ+(xa)−ψ−(xa)]=ik+[ψ+(xb)−ψ−(xb)]. These two equations can be combined into a single matrix equation: \[\begin{bmatrix}1 & 1 \\ k...Hence, ik−[ψ+(xa)−ψ−(xa)]=ik+[ψ+(xb)−ψ−(xb)]. These two equations can be combined into a single matrix equation: [11k−−k−][ψ+(xa)ψ−(xa)]=[11k+−k+][ψ+(xb)ψ−(xb)]. After doing a matrix inversion, this becomes \[\Psi_b = \mathbf{M}_s(k_+,k_-) \, \Psi_a, \;\;\;\mathrm{where}\…
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Walet)/06%3A_Scattering_from_Potential_Steps_and_Square_Barriers/6.02%3A_Potential_step\begin{align} ϕ_I (x) &= A 0 e^{ i k_0 x} + B_0 e^{ − i k_0 x} , \label{6.7} \\[5pt] ϕ_{II} (x) &= A_1 e^{ i k_1 x} . \label{6.8} \end{align} We define a transmission (T) and reflection (R...\begin{align} ϕ_I (x) &= A 0 e^{ i k_0 x} + B_0 e^{ − i k_0 x} , \label{6.7} \\[5pt] ϕ_{II} (x) &= A_1 e^{ i k_1 x} . \label{6.8} \end{align} We define a transmission (T) and reflection (R) coefficient as the ratio of currents between reflected or transmitted wave and the incoming wave, where we have canceled a common factor \begin{align} A_1 &= \dfrac{2 k_0}{ k_0 + k_1 A_0} \label{6.12} \\[5pt] B_0 &= \dfrac{k_0 − k_1 }{k_0 + k_1 A_0} , \label{6.13} \end{align}
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_and_Applications_(Staelin)/07%3A_TEM_transmission_lines/7.02%3A_TEM_lines_with_junctionsThis page covers boundary value problems in transmission lines, emphasizing the uniqueness theorem and steps to resolve these issues through wave behavior and boundary conditions. It explains lossless...This page covers boundary value problems in transmission lines, emphasizing the uniqueness theorem and steps to resolve these issues through wave behavior and boundary conditions. It explains lossless TEM transmission lines and their wave equations, introduces reflection and transmission coefficients, and examines the behavior of standing waves and load impedance.
