Esposito G., Marmo G., Miele G., Sudarshan G. Advanced Concepts in Quantum Mechanics

Cambridge University Press, 2015. — 384 p. — ISBN: 1107076048.Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.Introduction: the need for a quantum theory
Experimental foundations of quantum theory
Waves and particles
Schrödinger picture, Heisenberg picture and probabilistic aspects
Integrating the equations of motion
Elementary applications: 1-dimensional problems
Elementary applications: multidimensional problems
Coherent states and related formalism
Introduction to spin
Symmetries in quantum mechanics
Approximation methods
Modern pictures of quantum mechanics
Formulations of quantum mechanics and their physical implications
Exam problems
Glossary of geometric concepts