Quasi-exact-solution of the Generalized Exe Jahn-Teller Hamiltonian

We consider the solution of a generalized Exe Jahn-Teller Hamiltonian in the context of quasi-exactly solvable spectral problems. This Hamiltonian is expressed in terms of the generators of the osp(2,2) Lie algebra. Analytical expressions are obtained for eigenstates and eigenvalues. The solutions lead to a number of earlier results discussed in the literature. However, our approach renders a new understanding of ``exact isolated'' solutions

The effect of a year of high-school biology on achievement in first-semester college biology

Thesis (Ed.M.)--Boston University, 1947. This item was digitized by the Internet Archive

Radial inflow turbine meshing rev. 1

This report describes meshing utilities to support the mesh generation for Radial Inflow Turbines. This includes two tools: (a) parameterised mesh generator for Nozzle Guide Vanes; (b) a geometry and mesh generation tool for turbine rotors. A key feature of the turbine rotor mesh and geometry generation tool is that it allows a parametric definition of the geometry based on properties of the aerodynamic passage. For example desired flow direction and evolution of flow area. This is in contrast to alternative methods, which start by defining the physical features of the rotor (e.g. hub and shroud shape), in which case the aerodynamic passage becomes and output. In addition to providing the description of the two tools, usage instructions and examples are provided

Symmetry breaking in the self-consistent Kohn-Sham equations

The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high temperatures and this solution is a uniform particle density. We show that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely the conditions when it can be observed and how to construct these non-uniform solutions. Two concrete examples are provided, including fermions on the sphere which are shown to crystallize in a structure that resembles the C$_{60}$ molecule.Comment: a few typos eliminate

Jahn-Teller instability in C6H6+ and C6H6- revisited

The benzene cation (C6H6+) has a doublet (e_{1g}) ground state in hexagonal ring (D_{6h}) geometry. Therefore a Jahn-Teller (JT) distortion will lower the energy. The present theoretical study yields a model Huckel-type Hamiltonian that includes the JT coupling of the e_{1g} electronic ground state with the two e_{2g} vibrational modes: in-plane ring-bending and C-C bond-stretching. We obtain the JT couplings from density functional theory (DFT), which gives a JT energy lowering of 970 cm^{-1} in agreement with previous quantum chemistry calculations. We find a non-adiabatic solution for vibrational spectra and predict frequencies shifts of both the benzene cation and anion, and give a reinterpretation of the available experimental data.Comment: 6 pages, 3 figure