Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor

► In this Letter we study the exact quantum evolution for continuous spectra problems. ► We base our discussion on the use of the Weyl eigendifferentials. ► We give a generalized Lewis and Riesenfeld phase for continuous spectra. ► This generalized phase or Aharonov-Anandan geometric phase is linked to the S matrix. ► The modified Pöschl-Teller and the linear potential are worked out as illustrations.