A time-dependent microscopic approach to the scission process, i.e., the transition from two fragments connected by a thin neck (αiαi) to two separated fragments (αfαf), which takes place in a short time interval ΔT, is presented. We follow the evolution from αiαi to αfαf of all occupied neutron states by solving numerically the two-dimensional time-dependent Schrödinger equation with time-dependent potential. Calculations are performed for mass divisions from AL=70AL=70 to AL=118AL=118 (ALAL being the light-fragment mass). The duration of the neck rupture ΔT is taken as parameter having values from 0.25×10−220.25×10−22 to 6×10−22 s6×10−22 s. The resulting scission-neutron multiplicities νscνsc and primary fragment excitation energies View the MathML sourceEsc⁎ are compared with those obtained in the frame of the sudden approximation (ΔT=0ΔT=0). As expected, the sudden approximation is an upper limit. For ΔT=10−22 sΔT=10−22 s, which is a realistic value, the time-dependent results are 15%15% to 20%20% below this limit. For transition times longer than 6×10−22 s6×10−22 s the adiabatic limit is reached. The probability and current densities of the unbound neutrons at scission are also calculated. They provide a detailed picture of the emission mechanism and a hint for the angular distribution of the scission neutrons with respect to the fission axis.