Advanced Topics in Quantum Mechanics

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.

Preface; 1. Propagator and resolvent; 2. The WKB method and non-perturbative effects; 3. The phase space formulation of quantum mechanics; 4. The path integral formulation of quantum mechanics; 5. Metastable states; Appendix A: Asymptotic series and Borel resummation; Appendix B: Special functions; Appendix C: Gaussian integration; References; Index.

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).