The practical method of applying the variation principle to the calculation of the energy of an atom demands a trial function which contains variable parameters. The previous work done using this approach was based on the use of some combination of hydrogenic wave functions containing parameters inserted in appropriate places. The present calculation of the energy of the eleven-electron atom has been brought about using this method.

A novel method for integrating the time-dependent Schrödinger equation is presented. The moving boundary truncation (MBT) method is a time-dependent adaptive method that can significantly reduce the number of grid points needed to perform accurate wave packet propagation while maintaining stability. Hydrodynamic quantum trajectories are used to adaptively define the boundaries and boundary conditions of a fixed grid. The result is a significant reduction in the number of grid points needed to perform accurate calculations. A variety of model potential energy surfaces are used to evaluate the method. Excellent agreement with fixed boundary grids was obtained for each example. By moving only the boundary points, stability was increased to the level of the full fixed grid. Variations of the MBT method are developed which allow it to be applied to any potential energy surface and used with any propagation method. A variation of MBT is applied to the collinear H+H₂ reaction (using a LEPS potential) to demonstrate the stability and accuracy. Reaction probabilities are calculated for the three dimensional non-rotating O(³P)+H₂ and O(³P)+HD reactions to demonstrate that the MBT can be used with a variety of numerical propagation techniques. / text

Continuous weak measurement provide a convenient way to gather information about a quantum system without the need to prepare huge ensembles of identical systems as required by standard quantum measurement theory. Even though weak measurement alter the dynamics of the wave function slightly, they nevertheless are a good tool to monitor the dynamics of the wave function in real time in the presence of certain perturbations, for example, sudden momentum kicks due to collisions with particles of a surrounding gas. With weak measurement it is possible to monitor the dynamics of the wave function without knowing it initially. The continuous monitoring can be employed to influence the dynamics by means of feedback. This thesis focuses on the numeric simulation of the continuous monitoring of the position of a free massive particle as well as a particle bound in the following one-dimensional potentials: harmonic and double well. The monitoring scheme involves estimating the wave function of the hydrogen atom initially and then applying the results of the weak measurement its position to update the estimate through a numerically simulated stochastic evolution. We also simulate evolution of the true wave function. The key highlights of this thesis include: discussion of an alternative way to derive the stochastic differential equations that govern the evolution of the true and estimated wave functions of the system, as well as the explanation of the second order numerical scheme. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2012.

Thesis (Ph.D.)--University of Melbourne, School of Physics, 2003. / Typescript (photocopy). Includes bibliographical references (leaves 121-132).

Thesis (Ph. D.)--University of Rhode Island, 2003. / Typescript. Includes bibliographical references (leaves 99-102).

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

No description available.

The method of spin projection was examined by developing and applying computer programs to calculate projected semi-empirical and ab initio unrestricted Hartree-Fock (UHF) wavefunctions. The electronic spectra of naphthalene, anthracene, naphthacene and pentacene were calculated using the Pariser-Pople-Parr (PPP) Π-electron approximations and both UHF and configurational interaction (CI) techniques. The results of both techniques were compared with experimentally determined spectra with reasonable agreement between the CI and projected UHF results. While the CI calculations generally produced lower energies for the triplet states than the UHF calculations, the spectra from UHF calculations were in somewhat better agreement with experiment. Anomalies encountered with degeneracies and the presence of open shell ground states are also discussed. The geometry of monohomocyclooctatetraene anion radical (MHCOT) was studied using spin projection of the UHF INDO wavefunction. The theoretical molecular geometry was varied until the experimental hyperfine coupling constants matched hyperfine constants obtained from using both projected and unprojected UHF wavefunctions. The two types of calculations resulted in slightly different energies and geometries with the projected calculations giving a higher energy for the doublet state; essentially no differences were noted in the bond orders obtained from the two types of calculations. The geometry from the projected calculations was a somewhat more strained conformation than the geometry from the unprojected calculation. Ab initio UHF calculations with spin projection were performed on H₂O(+) to compare the energies of pure spin states from ab initio multiconfigurational self-consistent field with CI. (MCSCF/CI) with those from spin projection. The MCSCF/CI calculations are superior to the UHF plus spin projection calculations. This result will always be observed when the UHF wavefunction is very close to a pure spin state before spin projection. The dissociation of CF₂O was studied using ab initio wavefunctions. The energies of the unprojected UHF wavefunctions were examined along with those for the dissociated CF₂ + O fragments. Good agreement exists between the calculated and experimental vertical ionization potentials for CF₂0 at the equilibrium geometry. / Doctor of Philosophy

Thesis (MSc)--University of Stellenbosch, 2007. / ENGLISH ABSTRACT: The dielectric-barrier discharge (DBD) is a source of non-equilibrium plasma that has seen widespread industrial application in recent years. A high-voltage arbitrary-waveform generator has been designed, built and characterised for the purpose of investigating the influence that the applied voltage waveform has on the operation of a DBD. The developed arbitrary-waveform generator is based on the principle of Fourier synthesis. Up to twenty Fourier components are generated by means of a digital circuit board, and then separately amplified by Class-AB amplifiers. Twenty step-up transformers are subsequently used to transform the Fourier components to higher voltages; the summation of the Fourier components are realised by the series connection of the transformer secondary sides. It was found that the digital generation of the Fourier components is very accurate and provides for the easy configuration of arbitrary waveforms. Furthermore, the amplification of the Fourier components by the Class-AB amplifiers introduces very little distortion. The principle of adding the Fourier components via the step-up transformers has been demonstrated; however, the large distributed capacitances of the transformers adversely affect the operation of the Class-AB amplifiers, leading to the introduction of distortion into the generated waveform. Furthermore, it was found that care had to be taken to limit the introduction of EMI through the system’s large ground plane. / AFRIKAANSE OPSOMMING: Die di¨elektriese versperringsontlading (DVO) is ’n bron van nie-ekwilibrium plasma wat in die afgelope jare wye toepassing in die nywerheid gevind het. ’n Arbitrˆere-golfvorm hoogspanningskragbron is ontwerp, gebou en gekarakteriseer, met die doel om die invloed wat die aangewende spanningsgolfvorm het op die werking van die DVO, te ondersoek. Die ontwikkelde arbitrˆere golfvormgenerator is gebaseer op die beginsels van Fourier samestelling. Tot twintig Fourier komponente word digitaal gegenereer, en dan afsonderlik versterk deur Klas-AB versterkers. Twintig transformators word dan gebruik om die Fourier komponente na ho¨er spannings te transformeer. Die sommasie van die Fourier komponente geskied deur die serieskakeling van die transformators se sekondˆere windings. Daar is bevind dat die digitale generasie van die Fourier komponente baie akkuraat is, en dat die arbitrˆere golfvorms maklik verstel kan word. Verder versterk die Klas-AB versterkers die Fourier komponente sonder enige noemenswaardige vervorming. Die gebruik van die transformators om die Fourier komponente saam te voeg, is gedemonstreer. Die groot verspreide kapasitansies van die transformators be¨ınvloed egter die funksioneering van die Klas-AB versterkers, wat lei tot ’n vervorming van die uittree. Daar is ook bevind dat die toetrede van EM versteurings deur die grondvlak van die sisteem problematies kan wees.

published_or_final_version / abstract / Physics / Doctoral / Doctor of Philosophy