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2 results

  • 2 - The WKB Method and Nonperturbative Effects

  • Marcos Mariño, Université de Genève
  • Book:
    Advanced Topics in Quantum Mechanics
    Published online:
    02 December 2021
    Print publication:
    09 December 2021, pp 31-113

  • Summary

    It gives a detailed and rigorous exposition of the WKB method in one dimension and its exact version, which includes nonperturbative effects in the Planck constant. This is illustrated in many examples, including the double-well potential. It also includes a description of the semiclassical quantization of higher-dimensional integrable systems, which are illustated by the Toda lattice.

Advanced Topics in Quantum Mechanics
  • Marcos Mariño
  • Published online:
    02 December 2021
    Print publication:
    09 December 2021
  • 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.