Decay theory of unstable quantum systems

The present review article is aimed at a clear formulation of the basic problematics of the decay and at a description of the various recent attempts to solve this delicate problem, illustrating both their successes and limitations. The organisation of the article is as follows. After a short summary of the classical description of the decay, a detailed study of the quantum non-decay probability is given. Then the peculiar dynamical situation leading to the formation of an unstable system is identified and the formal and physical aspects of the process are discussed. A detailed analysis is then made of the preparation procedure of an unstable system which is shown to amount to a localisation of the decay fragments within a distance of the order of the range of the forces acting between them. After this the discussion of the general properties of the non-decay probability at all times is completed.