Derivation of the Quantum Mechanical Momentum Operator in the Position Representation

I pedagogically show that the momentum operator in quantum mechanics, in the position representation, commonly known to be a derivative with respect to a spatial x-coordinate, can be derived by identifying momentum as the generator of space translations

Quantum Field Theory: An Introduction

This document is a set of notes I took on QFT as a graduate student at the University of Pennsylvania, mainly inspired in lectures by Burt Ovrut, but also working through Peskin and Schroeder (1995), as well as David Tong’s lecture notes available online. They take a slow pedagogical approach to introducing classical field theory, Noether’s theorem, the principles of quantum mechanics, scattering theory, and culminating in the derivation of Feynman diagrams

Derivation of the Cramer-Rao Bound

I give a pedagogical derivation of the Cramer-Rao Bound, which gives a lower bound on the variance of estimators used in statistical point estimation, commonly used to give numerical estimates of the systematic uncertainties in a measurement

Far-field resonance fluorescence from a dipole-interacting laser-driven cold atomic gas

We analyze the temporal response of the fluorescence light that is emitted from a dense gas of cold atoms driven by a laser. When the average interatomic distance is comparable to the wavelength of the photons scattered by the atoms, the system exhibits strong dipolar interactions and collective dissipation. We solve the exact dynamics of small systems with different geometries and show how these collective features are manifest in the scattered light properties such as the photon emission rate, the power spectrum and the second-order correlation function. By calculating these quantities beyond the weak (linear) driving limit, we make progress in understanding the signatures of collective behavior in these many-body systems. Furthermore, we shed light on the role of disorder and averaging on the resonance fluorescence, of direct relevance for recent experimental efforts that aim at the exploration of many-body effects in dipole–dipole interacting gases of atoms

A Critical Literacy Approach to Student Affairs Education

This article argues for the use of critical literacy as a critical pedagogy in student affairs practice. The authors describe how some currents of the student affairs literature have shifted toward a focus on student learning and critical approaches to student development and learning. Subsequently, they discuss the social turn in our understanding of literacy and a related move toward critical approaches to understanding literacy as a social practice. Finally, they present a synthesis of the literature, which results in considerations for approaching higher education student affairs contexts through a critical literacy framework, exposing gaps and areas for future theorizing and research

Out-Crossing Among Commercial Strains Of The Northern Quahog, Mercenaria Mercenaria: Survival, Growth And Implications For Selective Breeding

Because the accumulation of inbreeding within hatchery-propagated stocks of the hard clam, Mercenaria mercenaria (Linnaeus, 1758), could result in reduced growth and survival, we studied the potential for improving performance through out-crossing among existing hatchery strains. We produced all 10 possible out-crossed combinations among 5 strains of clams as well as all 5 pure parental strains simultaneously in the hatchery and measured their size at the time of metamorphosis (the spat stage) and at the end of a nursery period in mesh bags at a single field site (the seed stage). We then planted replicate plots of all fifteen strains at five field sites in Virginia, USA encompassing the range of salinity conditions used by commercial growers, and monitored growth and survival for two growing seasons. We found significant phenotypic differences among strains at the spat and seed stage, but different strains performed best at each stage. In the field we found significant site effects, strain effects and strain-by-site interactions, but there was no evidence of negative correlations in performance among sites indicating strong trade-offs that would be problematic for selective breeding. Three different linear contrasts designed to compare out-crossed and pure strains for each parental stock, test for nonadditive genetic effects within each pairing of different parental strains, and estimate the general combining ability of parental strains reveal a complex pattern. We found both inbreeding and out-breeding depression depending on the developmental stage of the clams and the parental strain examined. Within strain crosses generally produced larger spat but smaller seed. Out-crossed progeny were generally smaller at the spat stage than the average of their parental lines but larger at the seed stage. The two best performing parental strains had significant, positive, general combining abilities, whereas this measure was negative for the two worst parental strains. In the field, inbreeding depression was restricted to lines that showed poor pure strain performance, and these strains also showed poor general combining ability, whereas strains with good pure line performance showed out-breeding depression and good general combining ability. Only the poorest performing pure parental lines showed non-additive effects when we compared each out-crossed strain to the mean of its parental strains, suggesting that heterotic effects are unlikely to be useful for selective breeding. Finally, there were significant correlations between seed measurements and field performance indicating that it may be possible, in the context of selective breeding programs, to weed out inferior strains or families early in the life cycle

Microsatellite marker development and analysis in the eastern oyster (Crassostrea virginica): Confirmation of null alleles and non-Mendelian segregation ratios

Eighteen microsatellite markers were developed for the Crassostrea virginica nuclear genome, including di-, tri-, and tetranucleotide microsatellite repeat regions that included perfect, imperfect, and compound repeat sequences. A reference panel with DNA from the parents and four progeny of 10 full-sib families was used for a preliminary confirmation of polymorphism at these loci and indications of null alleles. Null alleles were discovered at three loci; in two instances, primer redesign enabled their amplification. Two to five representative alleles from each locus were sequenced to ensure that the targeted loci were amplifying. The sequence analysis revealed not only variation in the number of simple sequence repeat units, but also polymorphisms in the microsatellite flanking regions. A total of 3626 bp of combined microsatellite flanking region from the 18 loci was examined, revealing indels as well as nucleotide site substitutions. Overall, 16 indels and 146 substitutions were found with an average of 4.5% polymorphism across all loci. Eight markers were tested on the parents and 39-61 progeny from each of four families for examination of allelic inheritance patterns and genotypic ratios. Twenty-six tests of segregation ratios revealed eight significant departures from expected Mendelian ratios, three of which remained significant after correction for multiple tests. Deviations were observed in both the directions of heterozygote excess and deficiency