A time-dependent approach to the scission process, i.e., to the transition from two fragments connected by a thin neck (deformation αi) to two separated fragments (deformation αf) is presented. This transition is supposed to take place in a very short time interval ΔT. Our approach follows the evolution from αi to αf 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 = 70 to AL = 118 (AL being the light fragment mass) taking into account all neutron states (Ω = 1/2, 3/2, ..., 11/2) that are bound in 236U at αi. ΔT is taken as parameter having values from 0.25×10-22 to 6×10-22 s. The resulting scission neutron multiplicities νsc and primary fragments' excitation energies E* sc are compared with those obtained in the frame of the sudden approximation (ΔT = 0). As expected, shorter is the transition time more excited are the fragments and more neutrons are emitted, the sudden approximation being an upper limit. For ΔT = 10-22 which is a realistic value, the time dependent results are 20% below this limit. For transition times longer than 6×10-22 s the adiabatic limit is reached: No scission neutrons are emitted anymore and the excitation energy at αf is negligible.