Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to p2−ix3p^2-ix^3

We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-ix^3$ potential (Handy 2001) is applicable to complex rotated versions of the Hamiltonian. This has important implications for extension of the method in the analysis of resonant states, Regge poles, and general bound states in the complex plane (Bender and Boettcher (1998)).Comment: Submitted to J. Phys.

Generating Converging Bounds to the (Complex) Discrete States of the P2+iX3+iαXP^2 + iX^3 + i\alpha X Hamiltonian

The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is applied to the $H_\alpha \equiv P^2 + iX^3 + i\alpha X$ Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the $L^2$ states, as argued (through asymptotic methods) by Delabaere and Trinh (J. Phys. A: Math. Gen. {\bf 33} 8771 (2000)).Comment: Submitted to J. Phys.

Silicon oxide films grown and deposited in a microwave discharge

Growth and deposition of silicon dioxide films in microwave discharg

Managing professional identity within a changing market environment: New Zealand optometrists’ responses to the growth of corporate optometry

This research investigated the effects of changes in the market environment for optometry services and products on the professional identity of New Zealand optometrists. It explored three issues. First, ways participants’ location within either the independent or corporate sectors shaped their professional identities. Second, ways potential ethical conflicts between participants’ healthcare and retailing identities were resolved. Last, participants’ opinions concerning the future of their profession. Twelve male and fourteen female optometrists were interviewed. Nineteen participants worked within independent optometry practices. Seven worked within practices that were part of international optometry chains. Six participants were recent graduates, the rest experienced optometrists. All participants identified primarily as healthcare professionals. All recognised that practising optometry within a commercial market created the possibility of ethical conflicts between healthcare and business imperatives. There were differences in the ways participants managed this boundary, with participants working within corporate optometry seeming more comfortable with the business aspects of their profession. All participants thought the profession was changing and several suggested that the future of independent optometry was limited. The article concludes that recent changes within the market environment of optometry have heightened tensions between optometrists’ medical and entrepreneurial identities and contributed to changing work patterns within the profession.fals

Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential

Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging lower and upper bounds to a specific discrete state energy, once the signature property of the associated wavefunction is known. This method is particularly effective for multidimensional, bosonic ground state problems, since the corresponding wavefunction must be of uniform signature, and can be taken to be positive. Despite this, the vast majority of problems studied have been on unbounded domains. The important problem of an electron in an infinite quantum lens potential defines a challenging extension of EMM to systems defined on a compact domain. We investigate this here, and introduce novel modifications to the conventional EMM formalism that facilitate its adaptability to the required boundary conditions.Comment: Submitted to J. Phys.

STRUCTURAL CHANGE IN THE U.S. MEAT AND POULTRY INDUSTRIES

Market structure, concentration, meat industry, poultry industry, Industrial Organization,

CONSOLIDATION IN U.S. MEATPACKING

Meatpacking consolidated rapidly in the last two decades: slaughter plants became much larger, and concentration increased as smaller firms left the industry. We use establishment-based data from the U.S. Census Bureau to describe consolidation and to identify the roles of scale economies and technological change in driving consolidation. Through the 1970's, larger plants paid higher wages, generating a pecuniary scale diseconomy that largely offset the cost advantages that technological scale economies offered large plants. The larger plants' wage premium disappeared in the 1980's, and technological change created larger and more extensive technological scale economies. As a result, large plants realized growing cost advantages over smaller plants, and production shifted to larger plants.Concentration, consolidation, meatpacking, scale economies, structural change, Industrial Organization, Livestock Production/Industries,

Eigenvalues of PT-symmetric oscillators with polynomial potentials

We study the eigenvalue problem $-u^{\prime\prime}(z)-[(iz)^m+P_{m-1}(iz)]u(z)=\lambda u(z)$ with the boundary conditions that $u(z)$ decays to zero as $z$ tends to infinity along the rays $\arg z=-\frac{\pi}{2}\pm \frac{2\pi}{m+2}$, where $P_{m-1}(z)=a_1 z^{m-1}+a_2 z^{m-2}+...+a_{m-1} z$ is a polynomial and integers $m\geq 3$. We provide an asymptotic expansion of the eigenvalues $\lambda_n$ as $n\to+\infty$, and prove that for each {\it real} polynomial $P_{m-1}$, the eigenvalues are all real and positive, with only finitely many exceptions.Comment: 23 pages, 1 figure. v2: equation (14) as well as a few subsequent equations has been changed. v3: typos correcte

Generating Converging Eigenenergy Bounds for the Discrete States of the -ix^3 Non-Hermitian Potential

Recent investigations by Bender and Boettcher (Phys. Rev. Lett 80, 5243 (1998)) and Mezincescu (J. Phys. A. 33, 4911 (2000)) have argued that the discrete spectrum of the non-hermitian potential $V(x) = -ix^3$ should be real. We give further evidence for this through a novel formulation which transforms the general one dimensional Schrodinger equation (with complex potential) into a fourth order linear differential equation for $|\Psi(x)|^2$. This permits the application of the Eigenvalue Moment Method, developed by Handy, Bessis, and coworkers (Phys. Rev. Lett. 55, 931 (1985);60, 253 (1988a,b)), yielding rapidly converging lower and upper bounds to the low lying discrete state energies. We adapt this formalism to the pure imaginary cubic potential, generating tight bounds for the first five discrete state energy levels.Comment: Work to appear in J. Phys. A: Math & Ge