## Date of Completion

Spring 5-1-2020

## Thesis Advisor(s)

Robin Cote

## Honors Major

Physics

## Disciplines

Atomic, Molecular and Optical Physics

## Abstract

At low energies, scattering phase shifts, the difference in phases between the incoming and outgoing spherical waves in scattering, for different partial waves follow a similar pattern. The phase shift curves, which are a function of the angular momentum quantum number for different scattering energy, obtain resonances after reaching their maxima, and as energy is increased, these resonances become smaller and eventually disappear. Using numerical methods involving the use of Chebyshev polynomials, we solve the wave equation for a scattering potential to obtain the radial equation. From the radial equation we then find the scattering phase shift for a particular energy and partial wave. The numerical methods for this project are used through code in MATLAB. By analyzing the phase shifts across different partial waves, we seek to find a relation between the scattering energy and the shape of the phase shift curves related to the disappearance of resonances.

At low energies, scattering phase shifts, the difference in phases between the incoming and outgoing spherical waves in scattering, for different partial waves follow a similar pattern. The phase shift curves, which are a function of the angular momentum quantum number for different scattering energy, obtain resonances after reaching their maxima, and as energy is increased, these resonances become smaller and eventually disappear. Using numerical methods involving the use of Chebyshev polynomials, we solve the wave equation for a scattering potential to obtain the radial equation. From the radial equation we then find the scattering phase shift for a particular energy and partial wave. The numerical methods for this project are used through code in MATLAB. By analyzing the phase shifts across different partial waves, we seek to find a relation between the scattering energy and the shape of the phase shift curves related to the disappearance of resonances.

## Recommended Citation

Faezi, Kaaviyan, "Changes in the Scattering Phase Shifts for Partial Waves of Ultracold Particles at Different Energies" (2020). *Honors Scholar Theses*. 743.

https://digitalcommons.lib.uconn.edu/srhonors_theses/743