The Laplace method for energy eigenvalue problems in quantum mechanics

Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius method) and then an analytic continuation for the continuum states (if present). In this work, we present an alternative way to solve these problems, based on the Laplace method. This technique uses a similar procedure for the bound states and for the continuum states. It was originally used by Schroedinger when he solved for the wavefunctions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach for graduate students to learn and describe how it can be employed to solve all problems whose wavefunctions are represented in terms of confluent hypergeometric functions

Relation between crystal structure and optical properties in the correlated blue pigment YIn_1−xMn_xO₃

A material's properties and functionalities are determined by its chemical constituents and the atomic arrangement in which they crystallize. For the recently discovered pigment YIn1−xMnxO3, for instance, it had been surmised that its bright blue color owes to an unusual, trigonal bipyramidal, oxygen coordination of the manganese impurities. Here, we demonstrate that, indeed, a direct correspondence between details of the local Mn environment and the pigment's blue color holds: Combining realistic many-body calculations (dynamical mean-field theory to treat the quasi-atomic Mn-multiplets at low doping x=8%) with an effective medium description (Kubelka-Munk model to describe scattering in a milled pigment sample), we find that only a Mn-coordination polyhedra consisting of two distorted oxygen pyramids results in a diffuse reflectance commensurate with the experimental blue color. We motivate that the distortion of the bipyramid helps circumventing atomic selection rules, allowing for dipolar d−d transitions and creating the desired two-peak absorption profile

Stress-Induced Changes In Extracellular Dopamine And Serotonin In The Medial Prefrontal Cortex And Dorsal Hippocampus Of Prenatally Malnourished Rats

Prenatal protein malnutrition continues to be a significant problem in the world today. Exposure to prenatal protein malnutrition increases the risk of a number of neuropsychiatric disorders in adulthood including depression, schizophrenia and attentional deficit disorder. In the present experiment we have examined the effects of stress on extracellular serotonin (5-HT) and dopamine in the medial prefrontal cortex and dorsal hippocampus of rats exposed in utero to protein malnutrition. The medial prefrontal cortex and dorsal hippocampus were chosen as two limbic forebrain regions involved in learning and memory, attention and the stress response. Extracellular 5-HT and dopamine were determined in the medial prefrontal cortex and dorsal hippocampus of adult male Sprague-Dawley rats using dual probe in vivo microdialysis. Basal extracellular 5-HT did not differ between malnourished and well-nourished controls in either the medial prefrontal cortex or the dorsal hippocampus. Basal extracellular dopamine was significantly decreased in the medial prefrontal cortex of malnourished animals. Restraint stress (20 m) produced a significant rise in extracellular dopamine in the medial prefrontal cortex of well-nourished rats but did not alter release in malnourished rats. In malnourished rats, stress produced an increase in 5-HT in the hippocampus, whereas stress produced a decrease in 5-HT in the hippocampus of well-nourished rats. These data demonstrate that prenatal protein malnutrition alters dopaminergic neurotransmission in the medial prefrontal cortex as well as altering the dopaminergic and serotonergic response to stress. These changes may provide part of the bases for alterations in malnourished animals’ response to stress

Design and analysis report for the RL10-2B breadboard low thrust engine

The breadboard low thrust RL10-2B engine is described. A summary of the analysis and design effort to define the multimode thrust concept applicable to the requirements for the upper stage vehicles is provided. Baseline requirements were established for operation of the RL10-2B engine under the following conditions: (1) tank head idle at low propellant tank pressures without vehicle propellant conditioning or settling thrust; (2) pumped idle at a ten percent thrust level for low G deployment and/or vehicle tank pressurization; and (3) full thrust (15,000 lb.). Several variations of the engine configuration were investigated and results of the analyses are included

ANALYSIS OF THE AERIAL AND LANDING PHASES OF THE GRAND JETE

The purpose of this study was to quantify the ground reaction forces, moments of forces and moment powers during the landing from the ballet jump called the grand jete. In addition, the flight phase was examined to determine whether the illusion of linear motion occurred. Laws (2002) has stated that it is possible for dancers to give the illusion of "floating" or traveling linearly rather than parabolically during the flight phase of a grand jete by raising the arms and/or the legs at an appropriate speed

Advanced engine study program

A design and analysis study was conducted to provide advanced engine descriptions and parametric data for space transfer vehicles. The study was based on an advanced oxygen/hydrogen engine in the 7,500 to 50,000 lbf thrust range. Emphasis was placed on defining requirements for high-performance engines capable of achieving reliable and versatile operation in a space environment. Four variations on the expander cycle were compared, and the advantages and disadvantages of each were assessed. Parametric weight, envelope, and performance data were generated over a range of 7,500 to 50,000 lb thrust and a wide range of chamber pressure and nozzle expansion ratio

Cerebellar infarction requiring surgical decompression in patient with COVID 19 pathological analysis and brief review

© 2020 The Authors Background: This report and literature review describes a case of a COVID-19 patient who suffered a cerebellar stroke requiring neurosurgical decompression. This is the first reported case of a sub-occipital craniectomy with brain biopsy in a COVID-19 patient showing leptomeningeal venous intimal inflammation. Clinical description: The patient is a 48-year-old SARS-COV-2 positive male with multiple comorbidities, who presented with fevers and respiratory symptoms, and imaging consistent with multifocal pneumonia. On day 5 of admission, the patient had sudden change in mental status, increased C-Reactive Protein, ferritin and elevated Interleukin-6 levels. Head CT showed cerebral infarction from vertebral artery occlusion. Given subsequent rapid neurologic decline from cerebellar swelling and mass effect on his brainstem emergent neurosurgical intervention was performed. Brain biopsy found a vein with small organizing thrombus adjacent to focally proliferative intima with focal intimal neutrophils. Conclusion: A young man with COVID-19 and suspected immune dysregulation, complicated by a large cerebrovascular ischemic stroke secondary to vertebral artery thrombosis requiring emergent neurosurgical intervention for decompression with improved neurological outcomes. Brain biopsy was suggestive of inflammation from thrombosed vessel, and neutrophilic infiltration of cerebellar tissue