UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Comparative analysis of differential cross sections of pure and mixed states of spinless bosons Choi, Kang

Abstract

In this thesis, we examine a simple case where two nonidentical, spineless bosons scatter elastically from each other, assuming that their interaction is weak and thus only leading-order perturbation theory is valid. We derive two different formulae for the differential cross-sections when the projectile particle is initially in a quantum superposition of two pure states (pure state) and a mixed ensemble of the same two pure states (mixed state). We take into account the relativistic effects fully in principle, although we only focus on the low-energy limit in the formula in one of our examples, which can be interpreted as a non-relativistic approximation. First, the derivation was made assuming that both incoming and outgoing particles are plane waves, which will provide us with an approximation. Then, the differential cross-section was derived assuming that only the initial state of the projectile is a wave packet. Next, we compared the differential cross-sections when the projectile particles are in a pure state and a mixed state in several examples, including the Half-plane waves, waves in the double-slit experiment, and double Gaussian wave packets. Finally, we discussed the limiting cases and performed integrations over target momentum to obtain an inclusive differential cross-section with respect to the momentum of the projectile particle. The results show that decoherence alters the differential cross-section when the incoming projectile has a finite width in at least one dimension.

Item Media

Item Citations and Data

Rights

Attribution-NonCommercial-NoDerivatives 4.0 International