Advanced Topics in Quantum Mechanics

An advanced quantum mechanics textbook that provides a unique pedagogical introduction to high-level topics in the field.

Marcos Mariño (Author)

9781108495875, Cambridge University Press

Hardback, published 9 December 2021

400 pages
26.3 x 18.3 x 2.1 cm, 0.713 kg

'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

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.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ]