Saddle-point model of a quantum point contact
= Saddle-point model of a quantum point contact
{title2=$U=U_0-m^*\omega_x^2x^2/2+m^*\omega_y^2y^2/2$}
A locally separable potential with an unstable longitudinal maximum and stable transverse confinement. Mode $n$ sees barrier top $E_n=U_0+\hbar\omega_y(n+1/2)$ and transmission $T_n(E)=[1+\exp(-2\pi(E-E_n)/(\hbar\omega_x))]^{-1}$. It is a single-particle smooth-barrier model; interactions and bias-induced reshaping require additions.