Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Control of polymorphism in coronene by the application of magnetic fields

Coronene, a polyaromatic hydrocarbon, has been crystallized for the first time in a different polymorph using a crystal growth method that utilizes magnetic fields to access a unit cell configuration that was hitherto unknown. Crystals grown in magnetic field of 1 T are larger, have a different appearance to those grown in zero field and retain their structure in ambient conditions. We identify the new form, beta-coronene, as the most stable at low temperatures. As a result of the new supramolecular configuration we report significantly altered electronic, optical and mechanical properties.Comment: 32 pages, 17 figure

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

Crystallisation From Volatile Deep Eutectic Solvents

A new class of deep eutectic solvents are presented where one component of the system is inherently volatile, enabling a premeditated, auto-destructive capability which leads inexorably to a series of novel crystal structures. These volatile deep eutectic solvents are easily-formed liquids with a greatly depressed melting point and exhibit all of the physical characteristics of classical deep eutectic solvents, with the exception that the hydrogen-bond donor component is volatile when exposed to the atmosphere at room temperature. We demonstrate the effectiveness of this concept through the exquisite control of pharmaceutical polymorphism, among which is a more efficacious form of acetaminophen, which can be formed spontaneously for the first time at room temperature.Comment: 42 pages, 23 figures, 1 Tabl

Synthesis of a metal oxide by forming solvate eutectic mixtures and study of their synthetic performance under hyper- and hypo-eutectic conditions

The synthesis of YBa2Cu3O7−x (YBCO or 123) superconductor was carried out under hyper- and hypo-eutectic conditions with different ammonium compounds, i.e., ammonium nitrate, formate, acetate, carbonate, bicarbonate, and tetramethylammonium nitrate. The aim was to find more affordable synthetic pathways using highly available and cheaper compounds, as well as to study the crystal formation under no-carbon conditions when ammonium nitrate was employed. Best results were obtained when eutectic conditions were achieved, namely by ammonium nitrate and YBaCu nitrates in a 5:1 molar ratio (81% of the superconductor). Ammonium formate, acetate, carbonate, and bicarbonate did not produce eutectic mixes. Temperature analysis of the reaction carried out by ammonium nitrate/YBaCu nitrates indicated the formation of barium carbonate, despite no carbon source being used in this reaction. This phenomenon is further discussed in this work. Consequently, tetramethylammonium nitrate, as a chelator and carbon source, was used, providing >96% of the superconductor

Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge