Solvable model of a quantum particle in a detector

The interaction of a quantum particle with a gaseous detector is studied in the quantum-mechanical state space of the particle-detector system by means of a simple stationary scattering 3D model. The particle is assumed to interact with [Formula: see text] two-level point-like scatterers depicting the atoms of the detector. Due to the contact interaction, the particle scatters off the atoms in isotropic spherical waves. Remarkably, the Lippmann–Schwinger equation of this multiple scattering problem can be exactly solved in a nonperturbative way. The aim is to analyze the influence of the initial microstate of the detector on the observed outcome, and to understand the mechanism of track formation in gaseous detectors. It is shown that the differential cross-section of excitation must be large enough in the forward direction to get the formation of tracks. In addition, the relatively small influence of atomic positions is highlighted. These results are explained through a perturbative calculation.

Relativistic Lippmann–Schwinger equation as an integral equation

The relativistic Lippmann–Schwinger equation was earlier formulated in terms of the limit values of the corresponding resolvent. In the present paper, we write down the limit values of the resolvent in an explicit form, and so the relativistic Lippmann–Schwinger equation is presented as an integral equation. Using this integral equation, we investigate the stationary scattering problems (relativistic case, Dirac equation). We consider the dynamical scattering problems (relativistic case, Dirac equation) as well.