  For the first time we calculate the electron transmission phase through a
quantum point contact (QPC). The QPC is considered in the saddle point
approximation in the single-electron picture. We show that when the electron
energy is close to the height of the potential barrier the transmission-phase
depends linearly on the energy. The coefficient in the linear dependence is
logarithmically enhanced by the ratio of the height over the curvature of the
barrier potential. We compare the calculated transmission phase with the first
experimental measurements of the phase.
