Erwin Schrödinger and the rise of wave mechanics. III. Early response and applications

This article (Part III) deals with the early applications of wave mechanics to atomic problems—including the demonstration of the formal mathematical equivalence of wave mechanics with the quantum mechanics of Born, Heisenberg, and Jordan, and that of Dirac—by Schrödinger himself and others. The new theory was immediately accepted by the scientific community.This article (in three parts) is an expanded version of the Schrödinger Centenary Lecture delivered by me at CERN (Organisation Européenne pour la Recherche Nucléaire), 1211 Geneva 23, Switzerland, on July 30, 1987.     

BISTAB: A portable bifurcation and stability analysis package

A portable bifurcation and stability analysis package, called BISTAB, is described. The package is written in FORTRAN V and can follow the connected set of equilibrium curves for a system of nonlinear ordinary differential equations in the state × parameter space by varying a bifurcation parameter. The curves are traced from an initial point with the continuation method of Kubicek, and the tangent method of Keller is used to find initial points on bifurcating curves near simple bifurcation points. Linearized stability analysis, location of Hopf bifurcation points, and sorting of points for plotting are also supported. While the package contains no new numerical methods, the lack of a requirement for any derivative information higher than the Jacobian makes BISTAB computationally efficient and useful for applied problems where nonnumerical bifurcation analysis may be difficult.     

Electrical transport in bulk amorphous selenium

D.C. conductivity measurements have been made as a function of temperature and external electric field on bulk amorphous selenium. A decrease in the activation energy with increase of electric field has been observed. This has been interpreted in terms of a mixed, thermally activated and trap limited conduction process.     

The Calculations that Gave Einstein “Heart Palpitations”

In what follows, I reply to the preceding article by Michel Janssen and Robert Schulmann, which itself was a response to my article on One month in the history of the discovery of general relativity theory, published in the February 1998 issue of this journal. I stand by the historical analysis and conclusions presented in my original article.     

Conduction mechanism in amorphous Si films

dc conductivity as a function of temperature has been measured for as-evaporated and annealed films of amorphous Si, grown by the vacuum evaporation technique. The experimental data suggest that conduction in the higher temperature range (～175–300 K) is by the thermally activated holes in the localized states near the valence band edge while conduction in the lower temperature range (～77–175 K) is found to be thermally assisted tunnelling in the localized states near the Fermi level. The activation energy for both the processes is found to increase with an increase in the annealing temperature. The average hopping distance, calculated for conduction near the Fermi level, is also found to increase with an increase in the annealing temperature.     

Study of dielectric properties of styrene-acrylonitrile graphite sheets composites in low and high frequency region

Conducting polymer composites should have a high dielectric constant and a high dissipation factor in the low and high frequency regions if they are to be used in charge storing devices, decoupling capacitors and electromagnetic interference shielding applications. Currently, extensive research is being carried out to enhance the dielectric constants of graphite-polymer, ceramic powder-polymer, metal powder-polymer and nanotube-polymer composites in the low frequency region. In this paper, we present the dielectric properties of styrene-acrylonitrile (SAN)-graphite sheets (GS) composites in the low and high frequency ranges. SAN-GS composites were prepared by the mixing process and by the hot compression mold technique. The composites showed a high dielectric constant and a high dissipation factor in the low and radio frequency region. Furthermore, the EMI shielding properties of these composites are evaluated in the radio frequency range. The conductivity and the dielectric constant of the SAN/GS composites increased with the addition of GS composites, and followed the power law model of percolation theory. The dielectric constant and the dissipation factor of the composites were analyzed according to the low and high frequency region.     

Superposition of Quantum Confinement Energy (SQCE) model for estimating shell thickness in core-shell quantum dots: validation and comparison

A novel theoretical model based on superposition of core and shell band-gaps, termed as SQCE model, is developed and reported here, which enables one to estimate the shell thickness in a core-shell quantum dot (QD), which is critically important in deciding its optical and electronic properties. We apply the model to two experimental core-shell QD systems, CdSe-CdS and CdSe-ZnS, which we synthesize by microemulsion method. We synthesize and study two series of samples, R and S to study the optical properties. The core size is varied in the R-series (by varying water-to-surfactant ratio, R) whereas the shell thickness is varied in the S-series (by varying the shell-to-core precursor molar ratio, S). The core and core-shell QDs from R-series and S-series are characterized for particle size, shape and crystallographic information. The shell thickness for all core-shell QD samples is estimated by SQCE model, and experimentally measured with TEM and SAXS. A close match is observed between experimental values and model predictions, thus validating the model. Further, the optimum shell thickness (corresponding to maximum quantum yield) values for CdS and ZnS over a 4.26 nm CdSe core have been estimated as 0.585 nm and 0.689 nm, respectively, from the SQCE model. The SQCE model developed in this work is applicable to other core-shell quantum dots also, such as CdTe-CdS, CdTe-CdSe and CdS-ZnS, and will serve as a useful complement to experimental measurement.