The double well potential in quantum mechanics: a simple, numerically exact formulation

The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double well potentials that are accessible to the undergraduate student. We describe a method for obtaining the numerically exact eigenenergies and eigenstates for such a model, along with the energies obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact solution is accessible with elementary mathematics, though numerical solutions are required. We also find that the WKB approximation is remarkably accurate, not just for the ground state, but for the excited states as well.Comment: 10 pages, 4 figures; suitable for undergraduate courses in quantum mechanic

Wide-field LOFAR-LBA power-spectra analyses: Impact of calibration, polarization leakage and ionosphere

Contamination due to foregrounds (Galactic and Extra-galactic), calibration errors and ionospheric effects pose major challenges in detection of the cosmic 21 cm signal in various Epoch of Reionization (EoR) experiments. We present the results of a pilot study of a field centered on 3C196 using LOFAR Low Band (56-70 MHz) observations, where we quantify various wide field and calibration effects such as gain errors, polarized foregrounds, and ionospheric effects. We observe a `pitchfork' structure in the 2D power spectrum of the polarized intensity in delay-baseline space, which leaks into the modes beyond the instrumental horizon (EoR/CD window). We show that this structure largely arises due to strong instrumental polarization leakage ($\sim30\%$) towards {Cas\,A} ($\sim21$ kJy at 81 MHz, brightest source in northern sky), which is far away from primary field of view. We measure an extremely small ionospheric diffractive scale ($r_{\text{diff}} \approx 430$ m at 60 MHz) towards {Cas\,A} resembling pure Kolmogorov turbulence compared to $r_{\text{diff}} \sim3 - 20$ km towards zenith at 150 MHz for typical ionospheric conditions. This is one of the smallest diffractive scales ever measured at these frequencies. Our work provides insights in understanding the nature of aforementioned effects and mitigating them in future Cosmic Dawn observations (e.g. with SKA-low and HERA) in the same frequency window.Comment: 20 pages, 11 figures, accepted for publication in MNRA

Prospects for detecting the 21cm forest from the diffuse intergalactic medium with LOFAR

We discuss the feasibility of the detection of the 21cm forest in the diffuse IGM with the radio telescope LOFAR. The optical depth to the 21cm line has been derived using simulations of reionization which include detailed radiative transfer of ionizing photons. We find that the spectra from reionization models with similar total comoving hydrogen ionizing emissivity but different frequency distribution look remarkably similar. Thus, unless the reionization histories are very different from each other (e.g. a predominance of UV vs. x-ray heating) we do not expect to distinguish them by means of observations of the 21cm forest. Because the presence of a strong x-ray background would make the detection of 21cm line absorption impossible, the lack of absorption could be used as a probe of the presence/intensity of the x-ray background and the thermal history of the universe. Along a random line of sight LOFAR could detect a global suppression of the spectrum from z>12, when the IGM is still mostly neutral and cold, in contrast with the more well-defined, albeit broad, absorption features visible at lower redshift. Sharp, strong absorption features associated with rare, high density pockets of gas could be detected also at z~7 along preferential lines of sight.Comment: 12 pages, 13 figures. MNRAS, in pres

Foregrounds for observations of the cosmological 21 cm line: I. First Westerbork measurements of Galactic emission at 150 MHz in a low latitude field

We present the first results from a series of observations conducted with the Westerbork telescope in the 140--160 MHz range with a 2 arcmin resolution aimed at characterizing the properties of the foregrounds for epoch of reionization experiments. For the first time we have detected fluctuations in the Galactic diffuse emission on scales greater than 13 arcmin at 150 MHz, in the low Galactic latitude area known as Fan region. Those fluctuations have an $rms$ of 14 K. The total intensity power spectrum shows a power--law behaviour down to $\ell \sim 900$ with slope $\beta^I_\ell = -2.2 \pm 0.3$. The detection of diffuse emission at smaller angular scales is limited by residual point sources. We measured an $rms$ confusion noise of $\sim$3 mJy beam$^{-1}$. Diffuse polarized emission was also detected for the first time at this frequency. The polarized signal shows complex structure both spatially and along the line of sight. The polarization power spectrum shows a power--law behaviour down to $\ell \sim 2700$ with slope $\beta^P_\ell = -1.65 \pm 0.15$. The $rms$ of polarization fluctuations is 7.2 K on 4 arcmin scales. By extrapolating the measured spectrum of total intensity emission, we find a contamination on the cosmological signal of $\delta T= \sqrt{\ell (\ell+1) C^I_\ell / 2\pi} \sim 5.7$ K on 5 arcmin scales and a corresponding $rms$ value of $\sim$18.3 K at the same angular scale. The level of the polarization power spectrum is $\delta T \sim 3.3$ K on 5 arcmin scales. Given its exceptionally bright polarized signal, the Fan region is likely to represent an upper limit on the sky brightness at moderate and high Galactic latitude.Comment: Minor corrections made to match the final version printed on A&A. A version with high resolution figures is available at http://www.astro.rug.nl/~bernardi/FAN/fan.pd

Polymorphism of alpha-1-antitrypsin in hematological malignancies

Alpha-1-antitrypsin (AAT) or serine protease inhibitor A1 (SERPINA1) is an important serine protease inhibitor in humans. The main physiological role of AAT is to inhibit neutrophil elastase (NE) released from triggered neutrophils, with an additional lesser role in the defense against damage inflicted by other serine proteases, such as cathepsin G and proteinase 3. Although there is a reported association between AAT polymorphism and different types of cancer, this association with hematological malignancies (HM) is, as yet, unknown. We identified AAT phenotypes by isoelectric focusing (in the pH 4.2-4.9 range) in 151 serum samples from patients with HM (Hodgkins lymphomas, non-Hodgkins lymphomas and malignant monoclonal gammopathies). Healthy blood-donors constituted the control group (n = 272). The evaluated population of patients as well as the control group, were at Hardy-Weinberg equilibrium for the AAT gene (χ2 = 4.42, d.f.11, p = 0.96 and χ2 = 4.71, d.f.11, p = 0.97, respectively). There was no difference in the frequency of deficient AAT alleles (Pi Z and Pi S) between patients and control. However, we found a significantly higher frequency of PiM1M1 homozygote and PiM1 allele in HM patients than in control (for phenotype: f = 0.5166 and 0.4118 respectively, p = 0.037; for allele: f = 0.7020 and 0.6360 respectively, p = 0.05). In addition, PiM homozygotes in HM-patients were more numerous than in controls (59% and 48%, respectively, p = 0.044). PiM1 alleles and PiM1 homozygotes are both associated with hematological malignancies, although this is considered a functionally normal AAT variant

Review of experience of family medicine in Europe and Central Asia : Executive summary

This report summarizes the findings of four case studies that review the experience of family medicine in Europe and Central Asia (ECA) Region. It is part of a study comprising five volumes that review the experience of family medicine in four countries in ECA--Armenia, Bosnia and Herzegovina, Kyrgyz Republic and Moldova. The report reviews the experience, draws lessons, and establishes an evidence base for detailed analysis. The study presents best practices for policy dialogue and future investments by the World Bank and other financial institutions. The detailed case studies compare these countries and draw common themes and issues. Comparisons are made with best-developed or existing models in the OECD and other countries in the Europe and Central Asia Region that have already undertaken family medicine reform

Analisis produktivitas dan kinerja lingkungan dengan menggunakan konsep green productivity (study kasus PT.ABC)

PT. ABC is a private company engaged in the provision of clean water services under the auspices of PT. Kaltim Prima Coal). Constraint occurs is in the process of drinking water treatment and wastewater sludge yield potential as a source of environmental pollution. Other problems also exist in the high BOD and Cod content of wastewater after measurement. As for the number of connections installed for corporate customers, there are only 2,895 connections, while from the data of PTABC, the company's connection target is 12,589, so from the total target of PT. ABC has only been able to obtain a connection of 23% of the target to be achieved. a need to increase water production by PT. ABC in order to increase the quantity of clean water production for all consumers. The concept of green productivity (GP) can be used in the search for solutions to increase productivity and protect the environment. The study begins by identifying the root cause of a lot of liquid waste and a low amount of water production, setting objectives and targets, choosing the resources and information available to arrange alternative green productivity. There are two alternatives, the selected alternative in this study are alternative 2 merge maximizing the raw water intake, repair Well Bore Tj.Bara , and the use of wastewater that is the use of waste as material raw returned by first applying multilevel aeration technology to reduce levels of COD and BOD5 in wastewater. based on the use of the cost benefit anlysis method the company's productivity and EPI increases if implementing this alternative will increase 40% from the initial production of 114% to 154%. And the initial EPI index total value of -20.8 increased to 18.8 so it rose 39.6 which indicates an increase in productivity and environmental performanc

The first power spectrum limit on the 21-cm signal of neutral hydrogen during the Cosmic Dawn at z=20-25 from LOFAR

Observations of the redshifted 21-cm hyperfine line of neutral hydrogen from early phases of the Universe such as Cosmic Dawn and the Epoch of Reionization promise to open a new window onto the early formation of stars and galaxies. We present the first upper limits on the power spectrum of redshifted 21-cm brightness temperature fluctuations in the redshift range z = 19.8-25.2 (54-68 MHz frequency range) using 14 h of data obtained with the LOFAR-Low Band Antenna (LBA) array. We also demonstrate the application of a multiple pointing calibration technique to calibrate the LOFAR-LBA dual-pointing observations centred on the North Celestial Pole and the radio galaxy 3C220.3, We observe an unexplained excess of similar to 30-50 per cent in Stokes / noise compared to Stokes V for the two observed fields, which decorrelates on greater than or similar to 12 s and might have a physical origin. We show that enforcing smoothness of gain errors along frequency direction during calibration reduces the additional variance in Stokes I compared Stokes V introduced by the calibration on sub-band level. After subtraction of smooth foregrounds, we achieve a 2 sigma upper limit on the 21-cm power spectrum of Delta(2)(21) &lt;(14561 mK)(2) at k similar to 0.038 h cMpc(-1) and Delta(2)(21) &lt;(14886 mK)(2) at k 0.038 h cMpc(-1) for the 3C220 and NCP fields respectively and both upper limits are consistent with each other. The upper limits for the two fields are still dominated by systematics on most k modes.</p

Structure in the Magnetic Field of the Milky Way Disk and Halo traced by Faraday Rotation

Magnetic fields in the ionized medium of the disk and halo of the Milky Way impose Faraday rotation on linearly polarized radio emission. We compare two surveys mapping the Galactic Faraday rotation, one showing the rotation measures of extragalactic sources seen through the Galaxy (from Hutschenreuter et al 2022), and one showing the Faraday depth of the diffuse Galactic synchrotron emission from the Global Magneto-Ionic Medium Survey. Comparing the two data sets in 5deg x 10deg bins shows good agreement at intermediate latitudes, 10 < |b| < 50 deg, and little correlation between them at lower and higher latitudes. Where they agree, both tracers show clear patterns as a function of Galactic longitude: in the Northern Hemisphere a strong sin(2 x longitude) pattern, and in the Southern hemisphere a sin(longitude + pi) pattern. Pulsars with height above or below the plane |z| > 300 pc show similar longitude dependence in their rotation measures. Nearby non-thermal structures show rotation measure shadows as does the Orion-Eridanus superbubble. We describe families of dynamo models that could explain the observed patterns in the two hemispheres. We suggest that a field reversal, known to cross the plane a few hundred pc inside the solar circle, could shift to positive z with increasing Galactic radius to explain the sin(2xlongitude) pattern in the Northern Hemisphere. Correlation shows that rotation measures from extragalactic sources are one to two times the corresponding rotation measure of the diffuse emission, implying Faraday complexity along some lines of sight, especially in the Southern hemisphere.Comment: 37 pages, 26 figures, Ap. J. accepte

The LOFAR Two-metre Sky Survey: Deep Fields: : II. The ELAIS-N1 LOFAR deep field

© ESO 2021.This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1051/0004-6361/202038828The LOFAR Two-metre Sky Survey (LoTSS) will cover the full northern sky and, additionally, aims to observe the LoTSS deep fields to a noise level of ~10 microJy/bm over several tens of square degrees in areas that have the most extensive ancillary data. This paper presents the ELAIS-N1 deep field, the deepest of the LoTSS deep fields to date. With an effective observing time of 163.7 hours, it reaches a root mean square (RMS) noise level below 20 microJy/bm in the central region (and below 30 microJy/bm over 10 square degrees). The resolution is 6 arcsecs and 84862 radio sources were detected in the full area (68 sq. deg.) with 74127 sources in the highest quality area at less than 3 degrees from the pointing centre. The observation reaches a sky density of more than 5000 sources per sq. deg. in the central ~5 sq. deg. region. We present the calibration procedure, which addresses the special configuration of some observations and the extended bandwidth covered (115 to 177 MHz; central frequency 146.2 MHz) compared to standard LoTSS. We also describe the methods used to calibrate the flux density scale using cross-matching with sources detected by other radio surveys in the literature. We find the flux density uncertainty related to the flux density scale to be ~6.5%. By studying the variations of the flux density measurements between different epochs, we show that relative flux density calibration is reliable out to about a 3 degree radius, but that additional flux density uncertainty is present for all sources at about the 3 per cent level; this is likely to be associated with residual calibration errors, and is shown to be more significant in datasets with poorer ionosphere conditions. We also provide intra-band spectral indices, which can be useful to detect sources with unusual spectral properties. The final uncertainty in the flux densities is estimated to be ~10% for ELAIS-N1.Peer reviewe