This book highlights the power and elegance of algebraic methods of solving problems in quantum mechanics. It shows that symmetries not only provide elegant solutions to problems that can be solved exactly, but also substantially simplify problems that must be solved approximately. Furthermore, the book provides an elementary exposition of quantum electrodynamics and its application to low-energy physics, along with a thorough analysis of the role of relativistic, magnetic, and quantum electrodynamic effects in atomic spectroscopy. Included are essential derivations made clear through detailed, transparent calculations. The book's commitment to deriving advanced results with elementary techniques, as well as its inclusion of exercises will enamor it to advanced undergraduate and graduate students.

The book is about the transition from classical to quantum mechanics, covering the historical development of this great leap, and explaining the concepts needed to understand it at a level suitable for undergraduate students. The first part of the book summarizes classical electrodynamics and the Hamiltonian formulation of classical mechanics, the two elements of classical physics which are crucial for understanding the classical to quantum transition. The second part loosely traces the historical development of the classical to quantum transition, starting with Einstein’s 1916 derivation of the Planck radiation law, continuing with the Ladenburg-Kramers-Born-Heisenberg dispersion theory and ending with Heisenberg’s magical 1925 paper which established quantum mechanics. The purpose of the book is partly historical, partly philosophical, but mainly pedagogical. It will appeal to a wide audience, from undergraduate students, for whom it can serve as a preparatory or supplementary text to standard textbooks, to physicists and historians interested in the historical development of science.