This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1992.
Geared toward upper-level undergraduates and graduate students, this self-contained first course in quantum mechanics covers basic theory and selected applications and includes numerous problems of varying difficulty. 1992 edition.
The history of quantum theory is a maze of conceptual problems. In this lucid and learned book, Olivier Darrigol tracks the role of formal analogies between classical and quantum theory, from Planck's first introduction of the quantum of action to Dirac's formulation of quantum mechanics. In so doing, Darrigol illuminates not only the history of quantum theory but also the role of analogies in scientific thinking and theory change. The most remarkable result of such analogical argument in quantum theory was Bohr's correspondence principle which, in Darrigol's words, "performed the acrobatic task of bridging two mutually contradictory theories (classical electrodynamics and atomic theory), without diminishing the contrast between them". By analyzing the origins, development, and applications of this principle, From c-Numbers to q-Numbers explains the remarkable fruitfulness of the research done under Bohr's guidance between 1916 and 1925 and shows why Heisenberg claimed that quantum mechanics was born as "a quantitative formulation of the correspondence principle". With a physicist's sure hand, Darrigol examines the formal and the epistemological aspects of the analogy between classical and quantum mechanics. Unlike previous works, which have tended to focus on qualitative, global arguments, he follows the lines of mathematical reasoning and symbolizing, and by doing so he is able to show the motivations of early quantum theorists more precisely - and provocatively - than ever before. For instance, Darrigol demonstrates that a universal principle of elementary chaos underlay Planck's analogies, and that Bohr's correspondence principle was related to his elaboration of a minimal-quantumtheoretical language. Most striking, Darrigol reveals how Dirac's personal conception of the relations among algebra, geometry, use of the analogy between c-numbers and and physics conditioned his highly creative q-numbers. Original, erudite, and witty, From c-Numbers to q-Numbers sets a new standard for the philosophically perceptive and mathematically precise history of quantum mechanics. For years to come it will influence historical and philosophical discussions of twentieth-century physics.
Innovative account of the origins of quantum mechanics told from a historical perspective, for advanced undergraduates, graduate students and researchers.
This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference 2005", an international conference in combinatorial number theory. The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics.
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.
