One-Dimensional Quantum Systems - From Few to Many Particles

TL;DR

This thesis develops analytical models and numerical methods to understand one-dimensional quantum systems from few to many particles, focusing on their configurations and interactions in harmonic traps for potential quantum applications.

Contribution

It introduces new analytical and numerical approaches to study one-dimensional quantum systems across different particle numbers, enhancing understanding of their configurations and interactions.

Findings

Analytical models for few-body systems in harmonic traps.

Numerical methods for many-body quantum systems.

Insights into particle configurations in strongly interacting regimes.

Abstract

In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical models and numerical methods both for the few- and many-body systems. One-dimensional systems are very interesting in a sense that particles aligned on a line can only change seats by going through each other. This property can be exploited in the strongly interacting regime, where particles are forced to sit in a specific configuration, which can be easily manipulated. The knowledge of how and where the particles are can be exploited in future quantum applications. In short, the thesis is about establishing a solid knowledge about everything that one needs to know about the one-dimensional few- and many-component interacting quantum systems trapped in harmonic oscillator potentials.