Quantum tomography as a new approach to simulating quantum processes

A new method is proposed for ab initio calculations of nonstationary quantum processes on the basis of a probability representation of quantum mechanics with the help of a positive definite function (quantum tomogram). The essence of the method is that an ensemble of trajectories associated with the characteristics of the evolution equation for the quantum tomogram. is considered in the space where the quantum tomogram is defined. The method is applied for detailed analysis of transient tunneling of a wave packet. The results are in good agreement with the exact numerical solution to the Schrodinger equation for this system. The probability density distributions are obtained in the coordinate and momentum spaces at consecutive instances. For transient tunneling of a wave packet, the probability of penetration behind the barrier and the time of tunneling are calculated as functions of the initial energy. (C) 2004 MAIK "Nauka/Interperiodica".