The bicomplex quantum Coulomb potential problem

Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper provides an analytical solution of the quantum Coulomb potential problem formulated in terms of bicomplex numbers. We define the problem by introducing a bicomplex hamiltonian operator and extending the canonical commutation relations to the form [X_i,P_k] = i_1 hbar xi delta_{ik}, where xi is a bicomplex number. Following Pauli's algebraic method, we find the eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained, along with appropriate eigenfunctions, by solving the extension of Schrodinger's time-independent differential equation. Examples of solutions are displayed. There is an orthonormal system of solutions that belongs to a bicomplex Hilbert space.Comment: Clarifications; some figures removed; version to appear in Can. J. Phy

Analysis of integration error in the ODP-L program and the effect of selenopotential parameters on the solution vector

Analysis of integration error in lunar orbit trajectory program and effect of selenopotential parameters on solution vecto

Intelligent states for angular momentum and Su(3) observables / by Benjamin R. Lavoie.

We generate expressions for all of the su(2) and su(3) intelligent states. To do so we combine well known coupling methods with unitary transformations; the construction is simple and efficient, and can be extended to generate intelligent states for any su(N) algebra. We also present a discussion of some of the properties of the su(2) and su(3) intelligent states

Slow Light in Metamaterial Waveguides

Metamaterials, which are materials engineered to possess novel optical properties, have been increasingly studied. The ability to fabricate metamaterials has sparked an interest in determining possible applications. We investigate using a metamaterial for boundary engineering in waveguides. A metamaterial-clad cylindrical waveguide is used to provide confinement for an optical signal, thereby increasing the local electromagnetic energy density. We show that metamaterial-clad waveguides have unique optical properties, including new modes, which we call hybrid modes. These modes have properties of both ordinary guided modes and surface plasmon-polariton modes. We show that for certain metamaterial parameters, the surface plasmon-polariton modes of a metamaterial-clad waveguide have less propagation loss than those of a metal-clad guide with the same permittivity. This low-loss mode is exploited for all-optical control of weak fields. Embedding three-level {\Lambda} atoms in the dielectric core of a metamaterial-clad waveguide allows the use of electromagnetically induced transparency to control an optical signal. Adjusting the pump field alters the group velocity of the signal, thereby controllably delaying pulses. Using the low-loss surface mode of a metamaterial-clad guide reduces losses by 20% over a metal cladding without sacrificing the group velocity reduction or confinement. In addition, we show that losses can be reduced by as much as 40% with sufficient reduction of the magnetic damping constant of the metamaterial. As this work aims for applications, practical considerations for fabricating and testing metamaterial-clad waveguides are discussed. An overview of the benefits and drawbacks for two different dielectric core materials is given. Also, a short discussion of other modes that could be used is given.Comment: PhD thesis, University of Calgary, November 2013. http://theses.ucalgary.ca//handle/11023/119

Composition dependent effects in gas chromatography

Fundamantal concepts are developed which are required to optimize a gas chromatograph-mass spectrometer chemical analysis system suitable for use on an unmanned roving vehicle for Mars exploration. Prior efforts have developed simulation models for the chromatograph which were compared with data obtained from a test facility. Representation of binary systems by superposition was shown to be a first-order approximation and in certain cases large discrepencies were noted. This subtask has as its objective generation of additional binary data and analysis of the observed nonlinear effects

Scale-by-scale energy budget in fractal element grid-generated turbulence

Measurements were conducted downstream of a square-fractal-element grid at , where L0 is the size of the largest element in the grid. The scale-by-scale energy budget for grid turbulence is used to investigate the phenomenological change in the turbulence between the inhomogeneous and homogeneous regions downstream of the grid, providing greater insight into the evolution of the turbulence in these two regions. It is shown that in the far field, x/L0 ? 20, where the flow is approximately homogeneous and isotropic, the scale-by-scale energy budget for grid turbulence is well balanced. In the near field, x/L0 < 20, the same energy budget is not satisfied, with the imbalance of the budget occurring at scales in the range ? ? r ? L0. It is proposed that the imbalance is caused by non-zero transverse transport of turbulent kinetic energy and production due to transverse mean velocity gradients. Approach of the spectra to k?5/3 behaviour with a decade long scaling range in the inhomogeneous region is attributed to forcing by these non-zero transverse terms