Exact results for `bouncing' Gaussian wave packets

We consider time-dependent Gaussian wave packet solutions of the Schrodinger equation (with arbitrary initial central position, x_0, and momentum, p_0, for an otherwise free-particle, but with an infinite wall at x=0, so-called bouncing wave packets. We show how difference or mirror solutions of the form psi(x,t)-psi(-x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate _t explicitly which illustrates how the free-particle kinetic (and hence total) energy is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, _t, and momentum, _t, and their relation to the impulsive force during the `collision' with the wall. Finally, the x_0,p_0 --> 0 limit is shown to reduce to a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands on the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form.Comment: 14 pages, 1 embedded .eps figur

The Stark effect in linear potentials

We examine the Stark effect (the second-order shift in the energy spectrum due to an external constant force) for two 1-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z>0 and V(z) infinite for z<0) and the symmetric linear potential (given by V(z) = F|z|). We show how straightforward use of the most obvious properties of the Airy function solutions and simple Taylor expansions give closed form results for the Stark shifts in both systems. These exact results are then compared to other approximation techniques, such as perturbation theory and WKB methods. These expressions add to the small number of closed-form descriptions available for the Stark effect in model quantum mechanical systems.Comment: 15 pages. To appear in Eur. J. Phys. Needs Institute of Physics (iopart) style file

Mode of onset of torsade de pointes in congenital long QT syndrome

Objectives.We sought to describe the mode of onset of spontaneous torsade de pointes in the congenital long QT syndrome.Background.Contemporary classifications of the long QT syndrome (LQTS) refer to the congenital LQTS as “adrenergic dependent” and to the acquired LQTS as “pause dependent.” Overlap between these two categories has been recognized, and a subgroup of patients with “idiopathic pause-dependent torsade” has been described. However, it is not known how commonly torsade is preceded by pauses in the congenital LQTS.Methods.We reviewed the electrocardiograms (ECGs) of all our patients with congenital LQTS evaluated for syncope or sudden death (30 patients). Documentation of the onset of torsade de pointes was available for 15 patients. All these patients had “definitive LQTS” by accepted clinical and ECG criteria.Results.Pause-dependent torsade de pointes was clearly documented in 14 of the 15 patients (95% confidence interval 68% to 100%). The cycle length of the pause leading to torsade was 1.3 ± 0.2 times longer than the basic cycle length, and most pauses leading to torsade were unequivocally longer than the preceding basic cycle length (80% of pauses were >80 ms longer than the preceding cycle length).Conclusions.The “long-short” sequence, which has been recognized as a hallmark of torsade de pointes in the acquired LQTS, plays a major role in the genesis of torsade in the congenital LQTS as well. Our findings have important therapeutic implications regarding the use of pacemakers for prevention of torsade in the congenital LQTS

IMPlementing IMProved Asthma self-management as RouTine (IMP2ART) in primary care: study protocol for a cluster randomised controlled implementation trial

BACKGROUND: Asthma is a common long-term condition and major public health problem. Supported self-management for asthma that includes a written personalised asthma action plan, supported by regular professional review, reduces unscheduled consultations and improves asthma outcomes and quality of life. However, despite unequivocal inter/national guideline recommendations, supported self-management is poorly implemented in practice. The IMPlementing IMProved Asthma self-management as RouTine (IMP2ART) implementation strategy has been developed to address this challenge. The aim of this implementation trial is to determine whether facilitated delivery of the IMP2ART strategy increases the provision of asthma action plans and reduces unscheduled care in the context of routine UK primary care. METHODS: IMP2ART is a parallel group, cluster randomised controlled hybrid II implementation trial. One hundred forty-four general practices will be randomly assigned to either the IMP2ART implementation strategy or control group. Following a facilitation workshop, implementation group practices will receive organisational resources to help them prioritise supported self-management (including audit and feedback; an IMP2ART asthma review template), training for professionals and resources to support patients to self-manage their asthma. The control group will continue with usual asthma care. The primary clinical outcome is the between-group difference in unscheduled care in the second year after randomisation (i.e. between 12 and 24 months post-randomisation) assessed from routine data. Additionally, a primary implementation outcome of asthma action plan ownership at 12 months will be assessed by questionnaire to a random sub-group of people with asthma. Secondary outcomes include the number of asthma reviews conducted, prescribing outcomes (reliever medication and oral steroids), asthma symptom control, patients' confidence in self-management and professional support and resource use. A health economic analysis will assess cost-effectiveness, and a mixed methods process evaluation will explore implementation, fidelity and adaptation. DISCUSSION: The evidence for supported asthma self-management is overwhelming. This study will add to the literature regarding strategies that can effectively implement supported self-management in primary care to reduce unscheduled consultations and improve asthma outcomes and quality of life. TRIAL REGISTRATION: ISRCTN15448074. Registered on 2 December 2019

Analytic results for Gaussian wave packets in four model systems: I. Visualization of the kinetic energy

Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium. We find, for specific choices of initial parameters, that as much as 90% of the kinetic energy can be localized (at least conceptually) in the `front half' of such Gaussian wave packets, and we visualize these effects.Comment: 22 pages, RevTeX, four .eps figures, to appear in Found. Phys. Lett. Vol. 17, Dec. 200

IMPlementing IMProved Asthma self-management as RouTine (IMP2ART) in primary care: study protocol for a cluster randomised controlled implementation trial.

BACKGROUND: Asthma is a common long-term condition and major public health problem. Supported self-management for asthma that includes a written personalised asthma action plan, supported by regular professional review, reduces unscheduled consultations and improves asthma outcomes and quality of life. However, despite unequivocal inter/national guideline recommendations, supported self-management is poorly implemented in practice. The IMPlementing IMProved Asthma self-management as RouTine (IMP2ART) implementation strategy has been developed to address this challenge. The aim of this implementation trial is to determine whether facilitated delivery of the IMP2ART strategy increases the provision of asthma action plans and reduces unscheduled care in the context of routine UK primary care. METHODS: IMP2ART is a parallel group, cluster randomised controlled hybrid II implementation trial. One hundred forty-four general practices will be randomly assigned to either the IMP2ART implementation strategy or control group. Following a facilitation workshop, implementation group practices will receive organisational resources to help them prioritise supported self-management (including audit and feedback; an IMP2ART asthma review template), training for professionals and resources to support patients to self-manage their asthma. The control group will continue with usual asthma care. The primary clinical outcome is the between-group difference in unscheduled care in the second year after randomisation (i.e. between 12 and 24 months post-randomisation) assessed from routine data. Additionally, a primary implementation outcome of asthma action plan ownership at 12 months will be assessed by questionnaire to a random sub-group of people with asthma. Secondary outcomes include the number of asthma reviews conducted, prescribing outcomes (reliever medication and oral steroids), asthma symptom control, patients' confidence in self-management and professional support and resource use. A health economic analysis will assess cost-effectiveness, and a mixed methods process evaluation will explore implementation, fidelity and adaptation. DISCUSSION: The evidence for supported asthma self-management is overwhelming. This study will add to the literature regarding strategies that can effectively implement supported self-management in primary care to reduce unscheduled consultations and improve asthma outcomes and quality of life. TRIAL REGISTRATION: ISRCTN15448074. Registered on 2 December 2019

Particle identification performance of a straw transition radiation tracker prototype

A 864 channel prototype of an integrated straw tracker and transition radiation detector for tracking and electron identification has been tested with and without magnetic field at the CERN SPS. The rejection against hadrons and converted photons has been measured and the dependence of the rejection power on detector parameters has been investigated. Tracking and hadron rejection were also studied in a high multiplicity environment. The results are compared with Monte-Carlo simulations. Wherever possible, conclusions are drawn concerning the performance of a full-scale detector at the future Large Hadron Collider