Numerical modelling of explicitly time-dependent quantum systems with δ-potentials

This paper can serve as an illustration for a course on quantum mechanics. It gives a non-trivial example of the time evolution of a system, which includes a particle in the potential of two delta -traps: one of which is in the fixed position, and the other moves with constant velocity. The numerical solution of the Schrodinger equation represents the behaviour of the vector of state in quite a transparent way; one can see rough pictures of the processes of charge transfer and ionization. The numerical procedure is explained, and an exercise can be carried out in constructing other time-dependent systems, containing delta -potentials.