Advanced Quantum Mechanics, the second volume on quantum mechanics by Franz Schwabl, discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic fields. As expected in Schwabl's works, the text features a compelling mathematical presentation in which all intermediate steps are derived and where numerous examples for application and exercises help the student to gain a thorough working knowledge of the subject. The treatment of relativistic wave equations and their symmetries and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear and elementary particle physics. This text extends and complements Schwabl's introductory Quantum Mechanics, which covers nonrelativistic quantum mechanics and offers a short treatment of the quantization of the radiation field.

This book covers advanced topics in quantum mechanics, including nonrelativistic multi-particle systems, relativistic wave equations, and relativistic fields. Numerous examples for application help readers gain a thorough understanding of the subject. The presentation of relativistic wave equations and their symmetries, and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear, and elementary particle physics. The authors earlier book, Quantum Mechanics, was praised for its unsurpassed clarity.

I. Nonrelativistic Many-Particle Systems.- 1. Second Quantization.- 2. Spin-1/2 Fermions.- 3. Bosons.- 4. Correlation Functions, Scattering, and Response.- II. Relativistic Wave Equations.- 5. Relativistic Wave Equations and their Derivation.- 6. Lorentz Transformations and Covariance of the Dirac Equation.- 7. Orbital Angular Momentum and Spin.- 8. The Coulomb Potential.- 9. The Foldy-Wouthuysen Transformation and Relativistic Corrections.- 10. Physical Interpretation of the Solutions to the Dirac Equation.- 11. Symmetries and Further Properties of the Dirac Equation.- III. Relativistic Fields.- 12. Quantization of Relativistic Fields.- 13. Free Fields.- 14. Quantization of the Radiation Field.- 15. Interacting Fields, Quantum Electrodynamics.- A Alternative Derivation of the Dirac Equation.- B Dirac Matrices.- B.1 Standard Representation.- B.2 Chiral Representation.- B.3 Majorana Representations.- C Projection Operators for the Spin.- C.1 Definition.- C.2 Rest Frame.- D The Path-Integral Representation of Quantum Mechanics 385 E Covariant Quantization of the Electromagnetic Field, the Gupta-Bleuler Method.- E.1 Quantization and the Feynman Propagator.- E.2 The Physical Significance of Longitudinal and Scalar Photons.- E.3 The Feynman Photon Propagator.- E.4 Conserved Quantities.- F Coupling of Charged Scalar Mesons to the Electromagnetic Field.