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Abstrak :
Self-adjoint extensions in quantum mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the naïve treatment. The necessary mathematical background is then built by developing the theory of self-adjoint extensions. Through examination of various quantum-mechanical systems, the authors show how quantization problems associated with the correct definition of observables and their spectral analysis can be treated consistently for comparatively simple quantum-mechanical systems. Systems that are examined include free particles on an interval, particles in a number of potential fields including delta-like potentials, the one-dimensional Calogero problem, the Aharonov–Bohm problem, and the relativistic Coulomb problem.

Abstrak :
Interferometry, the most precise measurement technique known today, exploits the wave-like nature of the atoms or photons in the interferometer. As expected from the laws of quantum mechanics, the granular, particle-like features of the individually independent atoms or photons are responsible for the precision limit, the shot noise limit. However this “classical” bound is not fundamental and it is the aim of quantum metrology to overcome it by employing entanglement among the particles. This work reports on the realization of spin-squeezed states suitable for atom interferometry. Spin squeezing was generated on the basis of motional and spin degrees of freedom, whereby the latter allowed the implementation of a full interferometer with quantum-enhanced precision.

Abstrak :
This work arises from our teaching this subject during many years. The vast majority of these exercises are the exams we gave to our students in this period. We carefully selected the subjects of the exercises to cover all the material which is most needed and which is treated in the most well known texts on these subjects. Each exercise is carefully solved in full details, explaining the theory behind the solution with particular care for those issues that, from our experience, are found most difficult from the average student. Indeed, several exercises are designed to throw light on aspects of the theory that, for one reason or another, are usually neglected with the result to make the students feel uneasy about them. In fact most students get acquainted just with the more common manipulations, which are illustrated by many examples in textbooks. Our exercises never require extensive calculations but tend to be somewhat unusual and force the solver to think about the problem starting from the principles, rather than by analogy with some previously solved exercise.

Abstrak :
Classical solutions play an important role in quantum field theory, high-energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important non perturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang–Mills instantons and on bounce solutions.