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Like rocket science or brain surgery, quantum mechanics is pigeonholed as a daunting and inaccessible topic, which is best left to an elite few. Authors have run the gamut from hand waving to heavy handed in hopes to dispel this common belief. This particular effort focuses on giving the reader an introduction, if not at least an appreciation of the role that linear algebra techniques play in the practical application of quantum mechanical methods. It includes a number of both worked and parallel applications.
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This book provides an introduction to Lie theory for first-year graduate students and professional physicists who may not have come across the theory in their studies. It is an overview of the theory of finite groups, a brief description of a manifold, and an informal development of the theory of one-parameter Lie groups. Interested readers should acquire a tool that is complete and that actually works to simplify or solve differential equations as well as moving them on to other topics.
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This book is the sequel to Lectures on Selected Topics in Mathematical Physics: Introduction to Lie Theory with Applications. This volume is devoted mostly to Lie groups, Lie algebras and generating functions, both for standard special functions and for the solution of certain types of physical problems.
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This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals that has evolved as part of the first semester of a course on theoretical and mathematical methods given to first- and second-year graduate students in physics and chemistry at the University of North Dakota. It introduces the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. The complex analytic properties are introduced naturally so that a more complete study becomes possible. Elliptic Functions and Elliptic Integrals is the first volume to be published from the lecture series Lectures on Selected Topics in Mathematical Physics from William A Schwalm.
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This volume explores the concept of the molecule as a meme, or idea, that had been accepted in the chemistry community and then diffused outwards into the wider scientific community creating? a new field of science, physical chemistry. View details

The history of how quantum mechanics was developed is a fascinating one and underlies the focus of this book; namely, given the rules that the founders of quantum mechanics developed, is it possible to find principles that lead to the structure of quantum mechanics as it was historically formulated? This is the first book in a series of works considering what particular relativity is applicable to a given dynamical theory. The series considers Newton, Einstein, and de Sitter relativities, while this book examines the unitary irreducible representations of the Galilei group and see how they provide the framework for Galilean quantum theory. View details

The intention of this book is to introduce ideas of how the visible world, and those parts of it that we cannot observe, either because they are too small or too large for our scale of perception, can be understood by consideration of only a few fundamental forces. My subject in these pages will be the authority of the commonly termed, laws of physics, which arise from the forces of nature, and the corresponding constants of nature. View details

We begin with a presentation of a minimal set of von Neumann postulates while introducing language and notation to facilitate subsequent discussion of quantum calculations based in finite-dimensional Hilbert spaces. We also address two-state quantum systems, entanglement of multiple two-state systems, quantum angular momentum theory and quantum approaches to statistical mechanics. A concluding chapter gives an overview of issues associated with quantum mechanics in continuous infinite-dimensional Hilbert spaces. View details

This book is the second in a series of volumes looking at what particular relativity is applicable to a given dynamical theory. This volume takes the point of view of a particle theory, based on the irreducible representations of the Poincare group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; we develop what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. View details

Measurements and experiments are made each and every day, but have you ever wondered why it is that a particular experiment has been designed to be the way it is? Anyone who is interested in the relationship between the precision and accuracy of measurements will find this volume useful. Whether you are a physicist, a chemist, a social scientist, or a student studying one of these subjects, this book will help identify the needle of useful data hidden in the haystack of obscuring background noise. View details

This book is a look at the origin of the molecular architecture of crystals; a topic that is becoming increasingly important and is often termed “crystal engineering”. It is a study of the means of predicting crystal structures and of designing crystals with particular properties by manipulating the structure and interaction of large molecules. That is, creating new crystal architectures with desired physical characteristics in which the molecules pack together in particular architectures; a subject of particular interest to the pharmaceutical industry.
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This book illustrates the complementarity of molecular beam (MB) spectra and ultracold molecule (UM) spectra in unraveling the complex electronic spectra of diatomic alkali metal molecules, using KRb as the prime example. Researchers interested in molecular spectroscopy, whether physicist, chemist, or engineer, may find this book helpful and may be able to apply similar ideas to their molecules of interest. View details

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This book presents simple interdisciplinary stochastic models meant as a gentle introduction to the field of non-equilibrium statistical physics. It focuses on the analysis of two-state models with cooperative effects and explores a variety of mathematical techniques to solve the master equations that govern these models. The models discussed are at the confluence of nanophysics, biology, mathematics and the social science, and they provide a pedagogical path toward understanding the complex dynamics of particle self-assembly with the tools of statistical physics.
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