Retrieving "Potential Energy Profile" from the archives

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1. Transmission Coefficient

   Linked via "potential energy profile"

   Context in Quantum Mechanics
   In the realm of quantum mechanics, specifically when analyzing scattering phenomena or time-independent bound states, the transmission coefficient is derived directly from the asymptotic behavior of the time-independent Schrödinger equation solution. For a one-dimensional system involving a potential energy profile $V(x)$, the transmission coefficient $T$ relates the flux density of the transmitted wave ($\mathbf{J}_T$) to t…