Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at the Calculational Details

In July 1925 Heisenberg published a paper [Z. Phys. 33, 879-893 (1925)] which ended the period of `the Old Quantum Theory' and ushered in the new era of Quantum Mechanics. This epoch-making paper is generally regarded as being difficult to follow, perhaps partly because Heisenberg provided few clues as to how he arrived at the results which he reported. Here we give details of calculations of the type which, we suggest, Heisenberg may have performed. We take as a specific example one of the anharmonic oscillator problems considered by Heisenberg, and use our reconstruction of his approach to solve it up to second order in perturbation theory. We emphasize that the results are precisely those obtained in standard quantum mechanics, and suggest that some discussion of the approach - based on the direct computation of transition amplitudes - could usefully be included in undergraduate courses in quantum mechanics.Comment: 24 pages, no figures, Latex, submitted to Am. J. Phy

Relational Contracting In A Digital Age; Panel Discussion

If, as it has sometimes been argued, changes in contract rules and theory are strongly affected by changes in economic conditions, we should note that the world has changed a good deal since the early 1960s when relational contract theory began to bloom. The economic world of 2004 is very different from the world of 1964. Modern relational contract theory was born about the same time as its great theoretical competitor, the rational choice approach of the legal economists. It came before the vast changes wrought by the information revolution and the increased globalization of the economy. What has relational theory taught us over the past forty years? How has it changed and adapted in light of those great economic changes? Where is it going in the future? Those were the general topics at a panel discussion which took place June 8, 2004, at the Oxstalls campus of the University of Gloucestershire in Gloucester, England. It was part of a conference entitled, The Common Law of Contracts as a World Force in Two Ages of Revolution, which marked the 150th anniversary of one of the most famous contracts cases of all time, Hadley v. Baxendale, and is the theme of the present Symposium. The Conference\u27s object was to explore how the common law adapts to and influences the kind of revolutionary changes that have swept over our society in the past forty years, and which swept over England in the forty years before Hadley v. Baxendale

Exploring EUV Spicules Using 304 Angstrom He II Data from SDO AIA

We present results from a statistical study of He II 304 Angstrom Extreme Ultraviolet (EUV) spicules at the limb of the Sun. We also measured properties of one macrospicule; macrospicules are longer than most spicules, and much broader in width than spicules. We use high-cadence (12 second) and high-resolution (0.6 arcseconds pixels) resolution data from the Atmospheric Imaging Array (AIA) instrument on the Solar Dynamic Observatory (SDO). All of the observed events occurred near the solar north pole, where quiet Sun or coronal hole environments ensued. We examined the maximum lengths, maximum rise velocities, and lifetimes of 33 Extreme Ultraviolet (EUV) spicules and the macrospicule. For the bulk of the Extreme Ultraviolet (EUV) spicules these quantities are, respectively, approximately 10,000-40,000 kilometers, 20-100 kilometers per second, and approximately 100- approximately 1000 seconds. For the macrospicule the corresponding quantities were respectively approximately 60,000 kilometers, approximately 130 kilometers per second, approximately 1800 seconds, which is typical of macrospicules measured by other workers. Therefore macrospicules are taller, longer-lived, and faster than most Extreme Ultraviolet (EUV) spicules. The rise profiles of both the spicules and the macrospicules match well a second-order ("parabolic" ) trajectory, although the acceleration was often weaker than that of solar gravity in the profiles fitted to the trajectories. Our macrospicule also had an obvious brightening at its base at birth, while such brightening was not apparent for the Extreme Ultraviolet (EUV) spicules. Most of the Extreme Ultraviolet (EUV) spicules remained visible during their descent back to the solar surface, although a small percentage of the spicules and the macrospicule faded out before falling back to the surface. Our sample of macrospicules is not yet large enough to determine whether their initiation mechanism is identical to that of Extreme Ultraviolet (EUV) spicules

Exploring He II 304 Angstrom Spicules and Macrospicules at the Solar Limb

No abstract availabl

Exploring He II 304 A Spicules and Macrospicules at the Solar Limb

No abstract availabl

Report of the AOD Format Task Force

The Analysis Object Data (AOD) are produced by ATLAS reconstruction and are the main input for most analyses. AOD, like the Event Summary Data (ESD, the other main output of reconstruction) are written as POOL files and are readable from Athena, and, to a limited extent, from ROOT. The AOD typical size, processing speed, and their relatively complex class structure and package dependencies, make them inconvenient to use for most interactive analysis. According to the computing model, interactive analysis will be based on Derived Physics Data (DPD), a user-defined format commonly produced from the AOD. As of release 12.0.3 it is common practice to write DPD as Athena-aware Ntuples (AANT) in ROOT. In an effort to organize and standardize AANT, we introduced the Structured Athena-aware Ntuple (SAN), an AANT containing objects that behave, as much as it is allowed by ROOT interpreter limitations, as their AOD counterparts. Recently it was proposed to extend SAN functionality beyond DPD implementation. SAN objects would be used as AOD objects. The TOB formed our task force with the mandate to "perform a technical evaluation of the two proposals, one based upon the existing AOD classes and architecture, the other upon Structured Athena-Aware Ntuples. [...] Criteria for the evaluation should include I/O performance, support for schema evolution, suitability for end user analysis and simplicity.

Improving the normalization of complex interventions: measure development based on normalization process theory (NoMAD): study protocol

<b>Background</b> Understanding implementation processes is key to ensuring that complex interventions in healthcare are taken up in practice and thus maximize intended benefits for service provision and (ultimately) care to patients. Normalization Process Theory (NPT) provides a framework for understanding how a new intervention becomes part of normal practice. This study aims to develop and validate simple generic tools derived from NPT, to be used to improve the implementation of complex healthcare interventions.<p></p> <b>Objectives</b> The objectives of this study are to: develop a set of NPT-based measures and formatively evaluate their use for identifying implementation problems and monitoring progress; conduct preliminary evaluation of these measures across a range of interventions and contexts, and identify factors that affect this process; explore the utility of these measures for predicting outcomes; and develop an online users’ manual for the measures.<p></p> <b>Methods</b> A combination of qualitative (workshops, item development, user feedback, cognitive interviews) and quantitative (survey) methods will be used to develop NPT measures, and test the utility of the measures in six healthcare intervention settings.<p></p> <b>Discussion</b> The measures developed in the study will be available for use by those involved in planning, implementing, and evaluating complex interventions in healthcare and have the potential to enhance the chances of their implementation, leading to sustained changes in working practices

Does a SLAP lesion affect shoulder muscle recruitment as measured by EMG activity during a rugby tackle?

Background: The study objective was to assess the influence of a SLAP lesion on onset of EMG activity in shoulder muscles during a front on rugby football tackle within professional rugby players. Methods: Mixed cross-sectional study evaluating between and within group differences in EMG onset times. Testing was carried out within the physiotherapy department of a university sports medicine clinic. The test group consisted of 7 players with clinically diagnosed SLAP lesions, later verified on arthroscopy. The reference group consisted of 15 uninjured and full time professional rugby players from within the same playing squad. Controlled tackles were performed against a tackle dummy. Onset of EMG activity was assessed from surface EMG of Pectorialis Major, Biceps Brachii, Latissimus Dorsi, Serratus Anterior and Infraspinatus muscles relative to time of impact. Analysis of differences in activation timing between muscles and limbs (injured versus non-injured side and non injured side versus matched reference group). Results: Serratus Anterior was activated prior to all other muscles in all (P = 0.001-0.03) subjects. In the SLAP injured shoulder Biceps was activated later than in the non-injured side. Onset times of all muscles of the noninjured shoulder in the injured player were consistently earlier compared with the reference group. Whereas, within the injured shoulder, all muscle activation timings were later than in the reference group. Conclusions: This study shows that in shoulders with a SLAP lesion there is a trend towards delay in activation time of Biceps and other muscles with the exception of an associated earlier onset of activation of Serratus anterior, possibly due to a coping strategy to protect glenohumeral stability and thoraco-scapular stability. This trend was not statistically significant in all cases