Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

Die Erschliessung der dritten Dimension. Entstehung und Entwicklung der zivilen Luftfahrtinfrastruktur in der Schweiz, 1919-1990

Weshalb liegt der grösste Flughafen der Schweiz heute in Zürich-Kloten? Welche Rolle spielte der Fluglärm bei der Entwicklung der Flughäfen Genf-Cointrin und Basel-Mülhausen? Wie entstanden in der Schweiz die ersten Luftstrassen und seit wann gibt es Fluglotsen? Erstmals wird die Geschichte der Flughäfen, der Flugplätze und der Flugsicherung in der Schweiz von den Anfängen bis zum Ende des 20. Jahrhunderts umfassend dargestellt. Der Autor fokussiert nicht auf einzelne Anlagen, sondern nimmt eine gesamtschweizerische Perspektive ein, die er in einen globalen Zusammenhang stellt. Aus dem umfangreichen Quellenmaterial rekonstruiert er die Entstehung und Entwicklung der Luftfahrtinfrastruktur in der Schweiz und beleuchtet die Auswirkung verschiedener Rahmenbedingungen und ­Akteure auf diese Entwicklung. Dabei berücksichtigt er ein breites Spektrum an Faktoren: beispielsweise die im Luftverkehr besonders wichtigen internationalen Einflüsse, den seit der Zwischenkriegszeit bestehenden Konkurrenzkampf zwischen den Flugplatzstandorten, die Rolle des Bundes oder die nach dem Zweiten Weltkrieg aufkommende Fluglärmthematik. Nebst den heute noch bestehenden Standorten werden auch längst aufgehobene Infrastrukturen sowie nie verwirklichte Projekte thematisiert, darunter der europäische Zentralflughafen für interkontinentale Grosswasserflugzeuge am Bodensee sowie die schweizerischen Zentralflughäfen in Bern-Utzenstorf und auf dem Neuenburgersee.

Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1 /| x | 2 . The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.

The Vacuolar H+-ATPase B1 Subunit Polymorphism p.E161K Associates with Impaired Urinary Acidification in Recurrent Stone Formers

Mutations in the vacuolar–type H+-ATPase B1 subunit gene ATP6V1B1 cause autosomal–recessive distal renal tubular acidosis (dRTA). We previously identified a single-nucleotide polymorphism (SNP) in the human B1 subunit (c.481G.A; p.E161K) that causes greatly diminished pump function in vitro. To investigate the effect of this SNP on urinary acidification, we conducted a genotype-phenotype analysis of recurrent stone formers in theDallas and Bern kidney stone registries. Of 555 patients examined, 32 (5.8%) were heterozygous for the p.E161K SNP, and the remaining 523 (94.2%) carried two wild–type alleles. After adjustment for sex, age, body mass index, and dietary acid and alkali intake, p.E161K SNP carriers had a nonsignificant tendency to higher urinary pH on a random diet (6.31 versus 6.09; P=0.09). Under an instructed low–Ca and low–Na diet, urinary pH was higher in p.E161K SNP carriers (6.56 versus 6.01; P,0.01). Kidney stones of p.E161K carriers were more likely to contain calcium phosphate than stones of wild-type patients. In acute NH4Cl loading, p.E161K carriers displayed a higher trough urinary pH (5.34 versus 4.89; P=0.01) than wild-type patients. Overall, 14.6% of wild-type patients and 52.4% of p.E161K carriers were unable to acidify their urine below pH 5.3 and thus, can be considered to have incomplete dRTA. In summary, our data indicate that recurrent stone formers with the vacuolar H+-ATPase B1 subunit p.E161K SNP exhibit a urinary acidification deficit with an increased prevalence of calcium phosphate– containing kidney stones. The burden of E161K heterozygosity may be a forme fruste of dRTA.

Normal values for pancreatic stone protein in different age groups.

BACKGROUND Pancreatic stone protein (PSP) has been identified as a promising sepsis marker in adults, children and neonates. However, data on population-based reference values are lacking. This study aimed to establish age-specific reference values for PSP. METHODS PSP was determined using a specific ELISA. PSP serum concentrations were determined in 372 healthy subjects including 217 neonates, 94 infants and children up to 16 years, and 61 adults. The adjacent categories method was used to determine which age categories had significantly different PSP concentrations. RESULTS PSP circulating levels were not gender-dependent and ranged from 1.0 to 99.4 ng/ml with a median of 9.2 ng/ml. PSP increased significantly between the age categories, from a median of 2.6 ng/ml in very preterm newborns, to 6.3 ng/ml in term newborns, to 16.1 ng/ml in older children (p < 0.001). PSP levels were higher on postnatal day three compared to levels measured immediately post delivery (p < 0.001). Paired umbilical artery and umbilical vein samples were strongly correlated (p < 0.001). Simultaneously obtained capillary heel-prick versus venous samples showed a good level of agreement for PSP (Rho 0.89, bias 19 %). CONCLUSIONS This study provides age-specific normal values that may be used to define cut-offs for future trials on PSP. We demonstrate an age-dependent increase of PSP from birth to childhood.