Computational physics

This thesis comprises two parts:Part I describes a method to improve the accuracy with which the polarization state of light can be characterized by the rotating quarter-wave plate technique. Through detailed analysis, verified by experiment, we determine the positions of the optic axes of the retarder and linear polarizer, and the wave plate retardance, to better than 1° for typical signal-to-noise ratios. Accurate determination of the Stokes parameters can be achieved using this technique to determine the precise retardance at each of the wavelengths of interest. In Part II, a theoretical analysis of the Fabry-Perot interferometer and its application to quantitative absorption spectroscopy is presented. Specifically the effects of broadening due to non-monochromatic light sources and examples of non-ideal etalon surfaces on the visibility of absorption features are investigated. The potential of this type of spectrometer for ethanol detection in a portable breath analysis application is discussed.

Author Keywords: ABSORPTION SPECTROSCOPY, CALIBRATION, FABRY-PEROT INTERFEROMETER, OPTICS, POLARIMETRY

The time-dependent Gross-Pitaevskii Equation, describing the movement of parti-

cles in quantum mechanics, may not be solved analytically due to its inherent non-

linearity. Hence numerical methods are of importance to approximate the solution.

This study develops a discrete scheme in time and space to simulate the solution

defined in a finite domain by using the Crank-Nicolson difference method and Sinc

Collocation Methods (SCM), respectively. In theory and practice, the time discretiz-

ing system decays errors in the second-order of accuracy, and SCMs are decaying

errors exponentially. A new SCM with a unique boundary treatment is proposed

and compared with the original SCM and other similar numerical techniques in time

costs and numerical errors. As a result, the new SCM decays errors faster than the

original one. Also, to attain the same accuracy, the new SCM interpolates fewer

nodes than the original SCM, which saves computational costs. The new SCM is

capable of approximating partial differential equations under different boundary con-

ditions, which can be extensively applied in fitting theory.

Author Keywords: Crank-Nicolson difference method, Gross-Pitaevskii Equation, Sinc-Collocation methods