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 epidemiology of observed temperament: Factor structure and demographic group differences

This study investigated the factor structure of observational indicators of children’s temperament that were collected across the first three years of life in the Family Life Project (N = 1205) sample. A four-factor model (activity level, fear, anger, regulation), which corresponded broadly to Rothbart’s distinction between reactivity and regulation, provided an acceptable fit the observed data. Tests of measurement invariance demonstrated that a majority of the observational indicators exhibited comparable measurement properties for male vs. female, black vs. white, and poor vs. not-poor children, which improved the generalizability of these results. Unadjusted demographic group comparisons revealed small to moderate sized differences (Cohen ds = |.23 – .42|) in temperamental reactivity and moderate to large sized differences (Cohen ds = −.64 – −.97) in regulation. Collectively, demographic variables explained more of the variation in regulation (R2 = .25) than in reactivity (R2 = .02 – .06). Follow-up analyses demonstrated that race differences were substantially diminished in magnitude and better accounted for by poverty. These results help to validate the distinction between temperamental reactivity and regulation using observational indicators

Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian 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 (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200

Amblyopia and quality of life: a systematic review

Background/Aims Amblyopia is a common condition which can affect up to 5% of the general population. The health-related quality of life (HRQoL) implications of amblyopia and/or its treatment have been explored in the literature. Methods A systematic literature search was undertaken (16th-30th January 2007) to identify the HRQoL implications of amblyopia and/or its treatment. Results A total of 25 papers were included in the literature review. The HRQoL implications of amblyopia related specifically to amblyopia treatment, rather than the condition itself. These included the impact upon family life; social interactions; difficulties undertaking daily activities; and feelings and behaviour. The identified studies adopted a number of methodologies. The study populations included; children with the condition; parents of children with amblyopia; and adults who had undertaken amblyopia treatment as a child. Some studies developed their own measures of HRQoL, and others determined HRQoL through proxy measures. Conclusions The reported findings of the HRQoL implications are of importance when considering the management of cases of amblyopia. Further research is required to assess the immediate and long-term effects of amblyopia and/or its treatment upon HRQoL using a more standardised approach

Spectral Statistics in the Quantized Cardioid Billiard

The spectral statistics in the strongly chaotic cardioid billiard are studied. The analysis is based on the first 11000 quantal energy levels for odd and even symmetry respectively. It is found that the level-spacing distribution is in good agreement with the GOE distribution of random-matrix theory. In case of the number variance and rigidity we observe agreement with the random-matrix model for short-range correlations only, whereas for long-range correlations both statistics saturate in agreement with semiclassical expectations. Furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal Gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes. By means of the Gutzwiller trace formula the trace of the cosine-modulated heat kernel is studied. Since the billiard boundary is focusing there are conjugate points giving rise to zeros at the locations of the periodic orbits instead of exclusively Gaussian peaks.Comment: 20 pages, uu-encoded ps.Z-fil

Identification of Radiopure Titanium for the LZ Dark Matter Experiment and Future Rare Event Searches

The LUX-ZEPLIN (LZ) experiment will search for dark matter particle interactions with a detector containing a total of 10 tonnes of liquid xenon within a double-vessel cryostat. The large mass and proximity of the cryostat to the active detector volume demand the use of material with extremely low intrinsic radioactivity. We report on the radioassay campaign conducted to identify suitable metals, the determination of factors limiting radiopure production, and the selection of titanium for construction of the LZ cryostat and other detector components. This titanium has been measured with activities of $^{238}$U$_{e}$~$<$1.6~mBq/kg, $^{238}$U$_{l}$~$<$0.09~mBq/kg, $^{232}$Th$_{e}$~$=0.28\pm 0.03$~mBq/kg, $^{232}$Th$_{l}$~$=0.25\pm 0.02$~mBq/kg, $^{40}$K~$<$0.54~mBq/kg, and $^{60}$Co~$<$0.02~mBq/kg (68\% CL). Such low intrinsic activities, which are some of the lowest ever reported for titanium, enable its use for future dark matter and other rare event searches. Monte Carlo simulations have been performed to assess the expected background contribution from the LZ cryostat with this radioactivity. In 1,000 days of WIMP search exposure of a 5.6-tonne fiducial mass, the cryostat will contribute only a mean background of $0.160\pm0.001$(stat)$\pm0.030$(sys) counts.Comment: 13 pages, 3 figures, accepted for publication in Astroparticle Physic

Vision in high-level football officials

YesOfficiating in football depends, at least to some extent, upon adequate visual function. However, there is no vision standard for football officiating and the nature of the relationship between officiating performance and level of vision is unknown. As a first step in characterising this relationship, we report on the clinically-measured vision and on the perceived level of vision in elite-level, Portuguese football officials. Seventy-one referees (R) and assistant referees (AR) participated in the study, representing 92% of the total population of elite level football officials in Portugal in the 2013/2014 season. Nine of the 22 Rs (40.9%) and ten of the 49 ARs (20.4%) were international-level. Information about visual history was also gathered. Perceived vision was assessed using the preference-values-assigned-to-global-visual-status (PVVS) and the Quality-of-Vision (QoV) questionnaire. Standard clinical vision measures (including visual acuity, contrast sensitivity and stereopsis) were gathered in a subset (n = 44, 62%) of the participants. Data were analysed according to the type (R/AR) and level (international/national) of official, and Bonferroni corrections were applied to reduce the risk of type I errors. Adopting criterion for statistical significance of p<0.01, PVVS scores did not differ between R and AR (p = 0.88), or between national- and international-level officials (p = 0.66). Similarly, QoV scores did not differ between R and AR in frequency (p = 0.50), severity (p = 0.71) or bothersomeness (p = 0.81) of symptoms, or between international-level vs national-level officials for frequency (p = 0.03) or bothersomeness (p = 0.07) of symptoms. However, international-level officials reported less severe symptoms than their national-level counterparts (p<0.01). Overall, 18.3% of officials had either never had an eye examination or if they had, it was more than 3 years previously. Regarding refractive correction, 4.2% had undergone refractive surgery and 23.9% wear contact lenses when officiating. Clinical vision measures in the football officials were similar to published normative values for young, adult populations and similar between R and AR. Clinically-measured vision did not differ according to officiating level. Visual acuity measured with and without a pinhole disc indicated that around one quarter of participants may be capable of better vision when officiating, as evidenced by better acuity (≥1 line of letters) using the pinhole. Amongst the clinical visual tests we used, we did not find evidence for above-average performance in elite-level football officials. Although the impact of uncorrected mild to moderate refractive error upon officiating performance is unknown, with a greater uptake of eye examinations, visual acuity may be improved in around a quarter of officials.Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UID/FIS/04650/2013

Studying Children's Intrapersonal Emotion Regulation Strategies from the Process Model of Emotion Regulation

peerreview_statement: The publishing and review policy for this title is described in its Aims & Scope. aims_and_scope_url: http://www.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=vgnt2