Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout.

'This volume dwells on three advanced and useful approaches to nonrelativistic quantum theory: the WKB method in exact form, phase-space quantization (Weyl--Wigner, Husimi), and path integrals. A majority of the covered topics are ignored by mainstream textbooks, making this text quite innovative. The exposition is comprehensive and pedagogically oriented, with numerous concrete examples detailed. This will prove a valuable textbook for academics and students aiming beyond basic quantum theory, to make them fluent and assist their teaching in several areas that actively serve in current research.' André Voros, Institut de Physique Théorique, CEA-Saclay, France

Marcos Mariño is Professor in Mathematical Physics at the University of Geneva. He has held postdoctoral positions at Yale, Rutgers and Harvard, and he was a junior staff researcher at the CERN Theory Division. His research focuses on mathematical aspects of quantum field theory and string theory. He has previously authored the book Instantons and Large N: An Introduction to Non-Perturbative Methods in Quantum Field Theory (Cambridge, 2015).