Wave packets in quantum theory of collisions

Details Wave packets in quantum theory of collisions Wave packets in quantum theory of collisions

2007-05-18

arxiv.org/abs/0705.2641v1

Physics

Quantum Physics

14 pages

Scientific paper

10.1134/S1063779608050067

Two methodological troubles of the quantum theory of collisions are considered. The first is the undesirable interference of the incident and scattered waves in the stationary approach to scattering. The second concerns the nonstationary approach to the theory of collisions of the type $a+b\to c+d$. In order to calculate the cross section one uses the matrix element $$ of the $S$-matrix. The element is proportional to $\delta$-function expressing the energy conservation. The corresponding probability $|< cd|S|ab>|^2$ contains $\delta^2$ which is mathematically senseless. The known regular way to overcome the difficulty seems to be unsatisfactory. In this paper, both the troubles are resolved using wave packets of incident particles.

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