A class of exactly solvable models for the Schrodinger equation

The final publication is available at Springer via the DOI in this recordWe present a class of confining potentials which allow one to reduce the one-dimensional Schroodinger equation to a named equation of mathematical physics, namely either Bessel's or Whittaker's differential equation. In all cases, we provide closed form expressions for both the symmetric and antisymmetric wavefunction solutions, each along with an associated transcendental equation for allowed eigenvalues. The class of potentials considered contains an example of both cusp-like single wells and a double-well.Engineering and Physical Sciences Research Council (EPSRC

On a solution of the Schrödinger equation with a hyperbolic double-well potential

Copyright © 2013 AIP PublishingWe report a solution of the one-dimensional Schrödinger equation with a hyperbolic double-well confining potential via a transformation to the so-called confluent Heun equation. We discuss the requirements on the parameters of the system in which a reduction to confluent Heun polynomials is possible, representing the wavefunctions of bound states.Engineering and Physical Sciences Research Council (EPSRC

Searching for confined modes in graphene channels: The variable phase method

Copyright © 2012 American Physical SocietyUsing the variable phase method, we reformulate the Dirac equation governing the charge carriers in graphene into a nonlinear first-order differential equation from which we can treat both confined-state problems in electron waveguides and above-barrier scattering problems for arbitrary-shaped potential barriers and wells, decaying at large distances. We show that this method agrees with a known analytic result for a hyperbolic secant potential and go on to investigate the nature of more experimentally realizable electron waveguides, showing that when the Fermi energy is set at the Dirac point, truly confined states are supported in pristine graphene. In contrast to exponentially decaying potentials, we discover that the threshold potential strength at which the first confined state appears is vanishingly small for potentials decaying at large distances as a power law; but nonetheless, further confined states are formed when the strength and spread of the potential reach a certain threshold.Millhayes Foundation (DAS)Engineering and Physical Sciences Research Council: EPSRC (CAD)EU FP7 ITN SpinoptronicsFP7 IRSES project SPINMETFP7 IRSES project TerACaNFP7 IRSES project ROBOCO

Excitons and interband terahertz transitions in narrow-gap carbon nanotubes

Copyright © 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.2013 International Conference on Electromagnetics in Advanced Applications (ICEAA), Torino, Italy, 9 - 13 September 2013Post-print versionWe show, via a solution of the quasi-one-dimensional two-body problem applied to a Dirac system, that excitonic effects suppress the one-dimensional Van Hove singularity in single-walled carbon nanotubes with narrow band gaps.EPSRC (CAD) [Engineering and Physical Sciences Research Council]EU FP7 ITN SpinoptronicsFP7 IRSES project SPIN-METFP7 IRSES project QOCaNFP7 IRSES project CANTOREngineering and Physical Sciences Research Council: EPSRC (CAD)EU FP7 ITN SpinoptronicsFP7 IRSES project SPIN-METFP7 IRSES project QOCaNFP7 IRSES project CANTO

Asymmetric coupling between two quantum emitters

We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the limiting case of chiral (or one-way) coupling. We investigate various quantum optical properties of the system, including its steady-state populations, power spectrum, and second-order correlation functions, and outline the characteristic features which emerge in each quantity as one sweeps through the nontrivial landscape of effective complex couplings. Most importantly, we reveal instances of population trapping, unexpected spectral features, and strong emission correlations

The reactivity of CO2 on the MgO(100) surface

We investigate the adsorption of CO2 over an MgO(001) terrace, as calculated using an embedded cluster method. We find adsorbed geometries for CO2 on the perfect surface with energies which differ appreciably from previous studies, and observe that it is polarization of the surface rather than the inclusion of electron correlation which leads to this discrepancy. Our results suggest that both monodentate and tridentate carbonate formation on the MgO(001) surface are favourable processes, with the monodentate structure being of lower energy. Adsorption of CO2 is found to be favourable at both F0 and F+ terrace sites, but not at F2+. We also find that chemisorption at oxygen vacancy sites with a single localized electron (F+) could provide a route for the conversion of CO2 to other products, and that this system may be a useful model for other, more effective catalysts

The Cholecystectomy As A Day Case (CAAD) Score: A Validated Score of Preoperative Predictors of Successful Day-Case Cholecystectomy Using the CholeS Data Set

Background Day-case surgery is associated with significant patient and cost benefits. However, only 43% of cholecystectomy patients are discharged home the same day. One hypothesis is day-case cholecystectomy rates, defined as patients discharged the same day as their operation, may be improved by better assessment of patients using standard preoperative variables. Methods Data were extracted from a prospectively collected data set of cholecystectomy patients from 166 UK and Irish hospitals (CholeS). Cholecystectomies performed as elective procedures were divided into main (75%) and validation (25%) data sets. Preoperative predictors were identified, and a risk score of failed day case was devised using multivariate logistic regression. Receiver operating curve analysis was used to validate the score in the validation data set. Results Of the 7426 elective cholecystectomies performed, 49% of these were discharged home the same day. Same-day discharge following cholecystectomy was less likely with older patients (OR 0.18, 95% CI 0.15–0.23), higher ASA scores (OR 0.19, 95% CI 0.15–0.23), complicated cholelithiasis (OR 0.38, 95% CI 0.31 to 0.48), male gender (OR 0.66, 95% CI 0.58–0.74), previous acute gallstone-related admissions (OR 0.54, 95% CI 0.48–0.60) and preoperative endoscopic intervention (OR 0.40, 95% CI 0.34–0.47). The CAAD score was developed using these variables. When applied to the validation subgroup, a CAAD score of ≤5 was associated with 80.8% successful day-case cholecystectomy compared with 19.2% associated with a CAAD score >5 (p < 0.001). Conclusions The CAAD score which utilises data readily available from clinic letters and electronic sources can predict same-day discharges following cholecystectomy