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Thesis--University of Florida. / Description based on print version record. Typescript. Vita. Bibliography: leaves 229-232.

Thesis (Ph. D.)--University of California, Santa Cruz, 1988. / Typescript. Includes bibliographical references.

Thesis (Ph. D.)--University of Oregon, 2006. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 204-213). Also available for download via the World Wide Web; free to University of Oregon users.

The quantum mechanical theory of rotational and vibrational transitions in atom-diatom systems is investigated and summarized. The time independent scattering formalism of Arthurs and Dalgarno is used, and the degeneracy-averaged cross section is expressed in terms of the scattering S matrix. The major emphasis is on the solution of the rotationally strongly coupled differential equations. Various methods of solving the scattering equations are examined and some of the inadequacies of these methods are discussed. A strong coupling (SC) approximation, valid for small energy exchange, is introduced and tested numerically on some model problems. A first-order iteration to the SC approximation is presented to improve the SC approximation and to extend the range of validity to cases of larger energy exchange. The SC results are compared with the accurate numerical solution and other approximate methods for some model problems. The comparison clearly demonstrates that the SC approximation is the computationally fastest, reasonably reliable method known for computing rotationally inelastic cross sections.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 91-92. / by François-Marc Turpin. / M.S.

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

The purpose of this thesis is to investigate the properties and wave velocities for an axially symmetric medium. The investigation consists of four parts. In the first part, the physical properties of the medium are defined. Then the stress-strain relations for the case under consideration are obtained from the general case. This is done by imposing the condition of symmetry on the strain energy function. Next the measurable constants are round in terms or the natural constants. This is done by applying simple extensions and shears to the material. After the measurable constants are determined in terms or the natural constants, then the relationship is inverted and the natural constants are found in terms or the measurable constants. Some elastic constants are then determined for an arbitrary direction, as it is not likely that the stresses will always be imposed along an axis of symmetry. Following this major part, the equations of motion for a vibrating medium are determined in terms or the natural constants by substituting the stress-strain relations. This is very straightforward, but must be done. The final step is made by finding the velocities of propagation of the waves by using the equations of motion. This is done by assuming a solution and substituting into the equations of motion. From these equations, a cubic equation defining the three principal velocities arises. The solution of this cubic equation is the culmination of this investigation. / M.S.

In this work, nondispersive wave packet solutions to linear partial differential equations are investigated. These solutions are characterized by infinite energy content; otherwise, they are continuous, nonsingular and propagate in free space without spreading out. Examples of such solutions are Berry and Balazs’ Airy packet, MacKinnon’s wave packet and Brittingham’s Focus Wave Mode (FWM). It is demonstrated in this thesis that the infinite energy content is not a basic problem per se and that it can be dealt with in two distinct ways. First these wave packets can be used as bases to construct highly localized, slowly decaying, time-limited pulsed solutions. In the case of the FWMs, this path leads to the formulation of the bidirectional representation, a technique that provides the most natural basis for synthesizing Brittingham-like solutions. This representation is used to derive new exact solutions to the 3-D scalar wave equation. It is also applied to problems involving boundaries, in particular to the propagation of a localized pulse in an infinite acoustic waveguide and to the launch ability of such a pulse from the opening of a semi-infinite waveguide. The second approach in dealing with the infinite energy content utilizes the bump-like structure of nondispersive solutions. With an appropriate choice of parameters, these bump fields have very large amplitudes around the centers, in comparison to their tails. In particular, the FWM solutions are used to model massless particles and are capable of providing an interesting interpretation to the results of Young’s two slit experiment and to the wave-particle duality of light. The bidirectional representation provides, also, a systematic way of deriving packet solutions to the Klein-Gordon, the Schrodinger and the Dirac equations. Nondispersive solutions of the former two equations are compared to previously derived ones, e.g., the Airy packet and MacKinnon's wave packet. / Ph. D.