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.

Control of Vertical Dimension During Rapid Palatal Expansion Using a High Pull Chin

Submitted in partial fulfillment of the requirements for a Certificate in Orthodontics, Dept. of Orthodontics, University of Connecticut Health Center, 1986

Die vierte Dimension

Anna Kellner

Exploring parents' memories of their child's death related sensory experiences as a dimension of grieving

Little is known about how dying children and their parents experience death. Dying children have reported death related sensory experiences (DRSEs), defined as seeing or hearing someone or something not visible or audible to others, associated with dying. Although parents report that they and the dying child benefit from these experiences, healthcare providers often unknowingly dismiss them. The aims of this phenomenological inquiry were to describe children's DRSEs and their meaning from the parents' perspectives. Four fathers and six mothers of African American, Caucasian, or Hispanic ethnicity, all Christian, ranging in age from 35 to 59 years, whose child died 23 to 52 months prior and was treated at a children's cancer center, were interviewed in the home or hospital setting of their choice. Children's ages at the time of their death ranged from 4 to 13 years. A modification of van Kaarn's phenomenological method of analysis was used to analyze data. Themes emerging from the data for the first aim were: perceiving someone or something from a spiritual realm others could not, expressing awareness tempered by parental reactions, and embracing transcendence. Themes emerging from the data for the second aim were: spiritual beings prepared child; child revealed reality, preparing parents; and child transcended wholly, easing parents' grief. Post-interview surveys revealed that parents found participating in this study a "very positive" or "positive" experience, particularly being able to tell the story of their child. Children's DRSEs have clinical implications for all who provide care near the end of life. Informing parents of DRSEs, cautioning that not all dying children express them, may help parents to anticipate this phenomenon, which may decrease anxiety when their child expresses them, increasing the opportunity for open dialogue between parent and child about dying and death, and decrease regrets associated with being unreceptive to their child's expressions of death awareness. Validating a child's DRSE can have profound effects on bereaved parents. Examining DRSEs from the child's perspective and the influence of informing parents of DRSEs on the dying experience of the child and the parental grieving process are recommended. ^