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Since the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics. The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.

Mathematical physics. --- Quantum physics. --- Mathematical Physics. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Mathematics

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This book presents a selection of Prof. Matteo Campanella’s writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule – one of the key principles of the probabilistic interpretation of quantum mechanics – that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category.

Mathematical physics. --- Quantum physics. --- Mathematical Applications in the Physical Sciences. --- Quantum Physics. --- Physical mathematics --- Physics --- Mathematics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics

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During the last thirty years a great advancement in low energy physics, particularly interactions of atoms with the electromagnetic field, has been achieved and the development of electronics and laser techniques has allowed to implement a fine manipulation of atoms with photons. A wealth of important applications has sprung out from the ability of manipulating large samples of cold atoms. Among them, the improvement of atomic clocks and the creation of atomic gyroscopes and of atomic gravity meters, which is obviously of great interest for geodesists and geophysicists, particularly for potential applications in satellite geodesy. This book explains the fundamental concepts necessary to understand atom manipulation by photons, including the principles of quantum mechanics. It is conceived as a road that leads the reader from classical physics (mechanics and electromagnetism, considered as a common scientific background of geodesists and geophysicists), to the basics of quantum mechanics in order to understand the dynamics of atoms falling in the gravity field, while interacting with suitably resonant laser beams. There are different types of measurements of gravity based on the manipulation of ultra-cold atoms; the book presents the principles of the instruments based on stimulated Raman transition, which can be easily worked out analytically. However, the concepts explained in the text can provide a good starting point to understand also the applications based on the so-called Block oscillations or on the Bose–Einstein condensation. .

Geophysics. --- Quantum physics. --- Magnetism. --- Magnetic materials. --- Geophysics/Geodesy. --- Quantum Physics. --- Magnetism, Magnetic Materials. --- Materials --- Mathematical physics --- Physics --- Electricity --- Magnetics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Geological physics --- Terrestrial physics --- Earth sciences --- Gravity --- Measurement. --- Gravimetry

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This proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theory and mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.

Mathematical analysis. --- Analysis (Mathematics). --- Operator theory. --- Quantum physics. --- Analysis. --- Operator Theory. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Functional analysis --- 517.1 Mathematical analysis --- Mathematical analysis --- Spectral theory (Mathematics) --- Mathematical physics

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This book is a historical analysis of the quantum mechanical revolution and the emergence of a new discipline from the perspective, not of a professor, but of a recent or actual Ph.D. student just embarking on an uncertain academic career in economically hard times. Quantum mechanics exploded on to the intellectual scene between 1925 and 1927, with more than 200 publications across the world, the majority of them authored by young scientists under the age of 30, graduate students or postdoctoral fellows. The resulting theory was a collective product that no single authority could claim, but it had a major geographical nod – the Copenhagen Institute of Theoretical Physics – where most of the informal, pre-published exchange of ideas occurred and where every participant of the new community aspired to visit. A rare combination of circumstances and resources – political, diplomatic, financial, and intellectual – allowed Niels Bohr to establish this “Mecca” of quantum theory outside of traditional and more powerful centres of science. Transitory international postdoctoral fellows, rather than established professors, developed a culture of research that became the source of major innovations in the field. Temporary assistantships, postdoctoral positions, and their equivalents were the chief mode of existence for young academics during the period of economic crisis and post-WWI international tensions. Insecure career trajectories and unpredictable moves through non-stable temporary positions contributed to their general outlook and interpretations of the emerging theory of quantum mechanics. This book is part of a four-volume collection addressing the beginnings of quantum physics research at the major European centres of Göttingen, Copenhagen, Berlin, and Munich; these works emerged from an expansive study on the quantum revolution as a major transformation of physical knowledge undertaken by the Max Planck Institute for the History of Science and the Fritz Haber Institute (2006–2012).

Physics. --- Quantum physics. --- History. --- History and Philosophical Foundations of Physics. --- Quantum Physics. --- History of Science. --- Annals --- Auxiliary sciences of history --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Quantum theory.