On random transformations of the wave function of a two-level system

The process of random diffusion variation of the wave function of a system with two states is analyzed. A method is developed for calculating the evolution operator and the damping increment of the probability distribution function of the state of the system on the basis of quaternion apparatus. It is proved analytically that the second moments formed from the wave function play the major role since all other statistical characteristics tend to equilibrium at a higher rate. For more general models of a random action, the result remains asymptotically the same, but the relative orders of increments may be different. Exceptional cases of incomplete statistical equilibrium are singled out. The possible role of the given model problem in the actual problem of state splitting in the transition from the microworld to macroworld is discussed. It is shown that, in spite of the views expressed in modern literature, the distribution of finite probabilities in the white noise model does not allow the well-known Schrodinger's Cat paradox to be resolved. (C) 2004 MAIK "Nauka/Interperiodica".