Within the context of Born-Infeld (BI) nonlinear electrodynamics (NED) we revisit the non-relativistic, spinless H-atom. The pair potential computed from the Born-Infeld equations is approximated by the Morse type potential with remarkable fit over the critical region where the convergence of both the short and long distance expansions slows down dramatically. The Morse potential is employed to determine both the ground state energy of the electron and the BI parameter.

An engaging and inspiring set of reflections by one of the master educators of today's Jewish world - full of delightful stories, compelling analysis and generosity of spirit. Read it and your faith in the Jewish future will be renewed. - Rabbi Lord Jonathan Sacks.

Durch eine Untersuchung der Stoßvorgänge wird die Auffassung entwickelt, daß die Quantenmechanik in der Schrödingerschen Form nicht nur die stationären Zustände, sondern auch die Quantensprünge zu beschreiben gestattet.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This excellent, semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, and more) and coverage of Einstein’s special and general theories of relativity, discussing the concept of simultaneity, kinematics, Einstein’s mechanics and dynamics, and more.

The notion of reality in the physical world has become, during the last century, somewhat problematic. The contrast between the simple and obvious reality of the innumerable instruments, machines, engines, and gadgets produced by our technological industry, which is applied physics, and of the vague and abstract reality of the fundamental concepts of physical science, as forces and fields, particles and quanta, is doubtlessly bewildering. There has already developed a gap between pure and applied science and between the groups of (...) men devoted to the one or the other activity, a separation that may lead to a dangerous estrangement. Physics needs a unifying philosophy, expressible in ordinary language, to bridge this gulf between "reality" as thought of in practice and in theory. I am not a philosopher but a theoretical physicist. I cannot provide a well balanced philosophy of science that would take due account of the ideas developed by differing schools, but I shall endeavor to formulate some ideas which have helped me in my own struggle with these problems. (shrink)

For this eighth edition he also wrote a new chapter on the quantum theory of solids.

In this collection of informal reminiscences, first published in 1975, Max Born has written an extraordinarily vivid account of his life and work, originally intended for his family. Ranging from his time at the University of Göttingen, where Born had his first real motivation for a professional career in science, to the period in Berlin as professor extraordinary, when he and his wife became close friends of Einstein, these anecdotes and memories chart the "heroic age of physics" from (...) the perspective of one of its leading characters. In 1954 Born was awarded the Nobel Prize in physics for his fundamental contributions to the great discovery of that cadre of superlative scientific minds – quantum theory. But his scientific research provides only one strand of this story. Born's varied interests outside science led to many interesting experiences – some of historical importance insofar as they offer a glimpse into German society before and between the wars. (shrink)

The purpose of this book, originally published in 1987, was to contribute to the advance of artificial intelligence by clarifying and removing the major sources of philosophical confusion at the time which continued to preoccupy scientists and thereby impede research. Unlike the vast majority of philosophical critiques of AI, however, each of the authors in this volume has made a serious attempt to come to terms with the scientific theories that have been developed, rather than attacking superficial 'straw men' which (...) bear scant resemblance to the complex theories that have been developed. For each is convinced that the philosopher's responsibility is to contribute from his own special intellectual point of view to the progress of such an important field, rather than sitting in lofty judgement dismissing the efforts of their scientific peers. The aim of this book is thus to correct some of the common misunderstandings of its subject. The technical term Artificial Intelligence has created considerable unnecessary confusion because of the ordinary meanings associated with it, and for that very reason, the term is endlessly misused and abused. The essays collected here all aim to expound the true nature of AI, and to remove the ill-conceived philosophical discussions which seek answers to the wrong questions in the wrong ways. Philosophical discussions and decisions about the proper use of AI need to be based on a proper understanding of the manner in which AI-scientists achieve their results; in particular, in their dependence on the initial planning input of human beings. The collection combines the Anglo-Saxon school of analytical philosophy with scientific and psychological methods of investigation. The distinguished authors in this volume represent a cross-section of philosophers, psychologists, and computer scientists from all over the world. The result is a fascinating study in the nature and future of AI, written in a style which is certain to appeal and inform laymen and specialists alike. has created considerable unnecessary confusion because of the ordinary meanings associated with it, and for that very reason, the term is endlessly misused and abused. The essays collected here all aim to expound the true nature of AI, and to remove the ill-conceived philosophical discussions which seek answers to the wrong questions in the wrong ways. Philosophical discussions and decisions about the proper use of AI need to be based on a proper understanding of the manner in which AI-scientists achieve their results; in particular, in their dependence on the initial planning input of human beings. The collection combines the Anglo-Saxon school of analytical philosophy with scientific and psychological methods of investigation. The distinguished authors in this volume represent a cross-section of philosophers, psychologists, and computer scientists from all over the world. The result is a fascinating study in the nature and future of AI, written in a style which is certain to appeal and inform laymen and specialists alike. inform laymen and specialists alike. (shrink)

In 1925-26, the late Max Born gave two sets of lectures at M.I.T., one on the structure of the atom, the other on the lattice theory of rigid bodies. Problems of Atomic Dynamics contains the text of both sets.What gives this volume its remarkable interest is just those dates: 1925-26. This must have been, by all accounts, the headiest period in twentieth-century physics, and Max Born was one of the leaders of the ferment. As Norbert Wiener remembers, "When (...) Professor Born came to the United States [for these lectures in 1925] he was enormously excited about the new basis Heisenberg had just given for the quantum theory of the atom."These lectures represent perhaps the most vivid written record of the transition between the "old" quantum theory of Bohr, and the "new" theory. "At the time I began this course of lectures," Born writes, "Heisenberg's first paper on the new quantum theory had just appeared. Here his masterly treatment gave the quantum theory an entirely new turn. The paper of Jordan and myself, in which we recognized the matrix calculus as the proper formulation of Heisenberg's ideas, was in press, and the manuscript of a third paper by the three of us was almost completed."Even as the lecture series progressed, Born became familiar with new results, which he introduced into his presentation: Pauli's fourth quantum number, Dirac's formalism, his own work on a general operational calculus. And yet, in spite of the conditions of revolutionary changes in physics that year -- in which established ancien regime principles were collapsing almost monthly -- the theory is developed with a cool elegance and with a formal completeness which may be regarded as a "limiting case" of its current state. These lectures represent the foundations of quantum theory, and they have withstood the tests of time -- the tests of more than forty years of experimental evidence. (shrink)

Dieses Buch ist bis heute eine der populärsten Darstellungen der Relativitätstheorie geblieben. In der vorliegenden Version haben J. Ehlers und M. Pössel vom Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) in Golm/Potsdam den Bornschen Text kommentiert und einen den anschaulichen, aber präzisen Stil Borns wahrendes, umfangreiches Ergänzungskapitel hinzugefügt, das die stürmische Entwicklung der Relativiatätstheorie bis hin zu unseren Tagen nachzeichnet. Eingegangen wird auf Gravitationswellen und Schwarze Löcher, auf neuere Entwicklungen der Kosmologie, auf Ansätze zu einer Theorie der Quantengravitation und auf die zahlreichen raffinierten (...) Experimente, welche die Gültigkeit der Einsteinschen Theorie mit immer größerer Genauigkeit bestätigt haben. Damit bleibt dieses Buch nach wie vor einer der unmittelbarsten Zugänge zur Relativitätstheorie für alle die sich für eine über das rein populärwissenschaftliche hinausgehende Einführung interessieren. (shrink)

The increasing digitalization in the field of psychological and educational testing opens up new opportunities to innovate assessments in many respects (e.g., new item formats, flexible test assembly, efficient data handling). In particular, computerized adaptive testing provides the opportunity to make tests more individualized and more efficient. The newly developed continuous calibration strategy (CCS) from Fink, Born, Spoden, and Frey (2018) makes it possible to construct computerized adaptive tests in application areas where separate calibration studies are not feasible. Due (...) to the goal of reporting on a common metric across test cycles, the equating is crucial for the CCS. The quality of the equating depends on the common items selected and the scale transformation method applied. Given the novelty of the CCS, the aim of the study was to evaluate different equating setups in the CCS and to derive practical recommendations. The impact of different equating setups on the precision of item parameter estimates and on the quality of the equating was examined in a Monte Carlo simulation, based on a fully crossed design with the factors common item difficulty distribution (bimodal, normal, uniform), scale transformation method (mean/mean, mean/sigma, Haebara, Stocking-Lord), and sample size per test cycle (50, 100, 300). The quality of the equating was operationalized by three criteria (proportion of feasible equatings, proportion of drifted items, and error of transformation constants). The precision of the item parameter estimates increased with increasing sample size per test cycle, but no substantial difference was found with respect to the common item difficulty distribution and the scale transformation method. With regard to the feasibility of the equatings, no differences were found for the different scale transformation methods. However, when using the moment methods (mean/mean, mean/sigma), quite extrem levels of error for the transformation constants A and B occurred. Among the characteristic curve method the performance of the Stocking-Lord method was slightly better than for the Haebara method. Thus, while no clear recommendation can be made with regard to the common item difficulty distribution, the characteristic curve methods turned out to be the most favorable scale transformation methods within the CCS. (shrink)

The aim of Werner Stegmaier’s Friedrich Nietzsche zur Einführung (Introduction to Nietzsche) is to introduce readers to Nietzsche’s thinking without reducing it to general theses or “doctrines.” Stegmaier thus provides not only an interpretation of Nietzsche’s philosophizing, but also a particular methodological approach to his works.The first part of the book, “Nietzsche’s Experiences,” provides a condensed account of Nietzsche’s life, including information about his family, friends, and acquaintances, his health, his philosophical influences, and the circumstances under which he wrote some (...) of his works. The second part, “Nietzsche’s Evaluations of the Significance of His Experiences for His Philosophizing,” .. (shrink)