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Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB…mehr
Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB approximations and Bohr-Sommerfeld quantization. Important modern topics and examples are also described, including Berry phase, quantum information, complexity and chaos, decoherence and thermalization, nonstandard statistics, as well as more advanced material such as path integrals, scattering theory, multiparticles and Fock space. Readers will gain a broad overview of Quantum Mechanics, as solid preparation for further study or research.
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Autorenporträt
Horäiu N¿stase is Researcher at the Institute for Theoretical Physics, State University of São Paulo. He completed his PhD at Stony Brook with Peter van Nieuwenhuizen, co-discoverer of Supergravity. While in Princeton as a postdoc, in a 2002 paper with David Berenstein and Juan Maldacena, he started the pp-wave correspondence, a sub-area of the AdS/CFT correspondence. He has written more than 100 scientific articles and 5 other books, including Introduction to the AdS/CFT Correspondence (2015), String Theory Methods for Condensed Matter Physics (2017), Classical Field Theory (2019), Introduction to Quantum Field Theory (2019), and Cosmology and String Theory (2019).
Inhaltsangabe
1. The mathematics of Quantum Mechanics 1: Finite dimensional Hilbert spaces 2. The mathematics of Quantum Mechanics 2: Infinite dimensional Hilbert spaces 3. The postulates of Quantum Mechanics and the Schrödinger equation 4. Two-level systems and spin 1/2, entanglement and computation 5. Position and momentum and their bases, canonical quantization, and free particles 6. The Heisenberg uncertainty principle and relations, and Gaussian wave packets 7. One dimensional problems in a potential V (x) 8. The harmonic oscillator 9. The Heisenberg picture and general pictures evolution operator 10. The Feynman path integral and propagators 11. The classical limit and Hamilton-Jacobi (the WKB method), Ehrenfest theorem 12. Symmetries in quantum mechanics I: Continuous symmetries 13. Symmetries in quantum mechanics II: Discrete symmetries and internal symmetries 14. Theory of angular momentum I: operators, algebras, representations 15. Theory of angular momentum II: addition of angular momenta and representations oscillator model 16. Applications of angular momentum theory: tensor operators, wave functions and the Schrödinger equation, free particles 17. Spin and L + S 18. The Hydrogen atom 19. General central potential and 3 dimensional (isotropic) harmonic oscillator 20. Systems of identical particles 21. Application of identical particles: He atom (2-electron system) and H2 molecule 22. Quantum mechanics interacting with classical electromagnetism 23. Aharonov-Bohm effect and Berry phase in quantum mechanics 24. Motion in a magnetic field, Hall effect and Landau levels 25. The WKB and semiclassical approximation 26. Bohr-Sommerfeld quantization 27. Dirac quantization condition and magnetic monopole s 28. Path integrals II: imaginary time and fermionic path integral 29. General theory of quantization of classical mechanics and (Dirac) quantization of constrained systems 30. Quantum entanglement and the EPR paradox 31. The interpretation of quantum mechanics and Bell's inequalities 32. Quantum statistical mechanics and tracing over a subspace 33. Elements of quantum information and quantum computing 34. Quantum complexity and quantum chaos 35. Quantum decoherence and quantum thermalization 36. Time-independent (stationary) perturbation theory: nondegenerate, degenerate, and formal cases 37. Time dependent perturbation theory: first order 38. Time-dependent perturbation theory: second and all orders 39. Application: interaction with (classical) electromagnetic field, absorption, photoelectric and Zeeman effect 40. WKB methods and extensions: state transitions and Euclidean path integrals (instantons) 41. Variational methods 42. Atoms and molecules, orbitals and chemical bonds: Quantum chemistry 43. Nuclear liquid droplet and shell models 44. Interaction of atoms with electromagnetic radiation: transitions and lasers 45. One-dimensional scattering, transfer and S matrices 46. Three dimensional Lippmann-Schwinger equation, scattering amplitudes and cross-sections 47. Born approximation and series, S- and T-matrix 48. Partial wave expansion, phase shift method and scattering length 49. Unitarity, optics and the optical theorem 50. Low energy and bound states, analytical properties of scattering amplitudes 51. Resonances and scattering, complex k and l 52. The semiclassical: WKB and eikonal approximations for scattering 53. Inelastic scattering 54. The Dirac equation 55. Multi-particle states in atoms and condensed matter: Schrödinger vs. occupation number 56. Fock space calculation with field operators 57. The Hartree-Fock approximation and other occupation number approximations 58. Nonstandard statistics: anyons and nonabelions.
1. The mathematics of Quantum Mechanics 1: Finite dimensional Hilbert spaces 2. The mathematics of Quantum Mechanics 2: Infinite dimensional Hilbert spaces 3. The postulates of Quantum Mechanics and the Schrödinger equation 4. Two-level systems and spin 1/2, entanglement and computation 5. Position and momentum and their bases, canonical quantization, and free particles 6. The Heisenberg uncertainty principle and relations, and Gaussian wave packets 7. One dimensional problems in a potential V (x) 8. The harmonic oscillator 9. The Heisenberg picture and general pictures evolution operator 10. The Feynman path integral and propagators 11. The classical limit and Hamilton-Jacobi (the WKB method), Ehrenfest theorem 12. Symmetries in quantum mechanics I: Continuous symmetries 13. Symmetries in quantum mechanics II: Discrete symmetries and internal symmetries 14. Theory of angular momentum I: operators, algebras, representations 15. Theory of angular momentum II: addition of angular momenta and representations oscillator model 16. Applications of angular momentum theory: tensor operators, wave functions and the Schrödinger equation, free particles 17. Spin and L + S 18. The Hydrogen atom 19. General central potential and 3 dimensional (isotropic) harmonic oscillator 20. Systems of identical particles 21. Application of identical particles: He atom (2-electron system) and H2 molecule 22. Quantum mechanics interacting with classical electromagnetism 23. Aharonov-Bohm effect and Berry phase in quantum mechanics 24. Motion in a magnetic field, Hall effect and Landau levels 25. The WKB and semiclassical approximation 26. Bohr-Sommerfeld quantization 27. Dirac quantization condition and magnetic monopole s 28. Path integrals II: imaginary time and fermionic path integral 29. General theory of quantization of classical mechanics and (Dirac) quantization of constrained systems 30. Quantum entanglement and the EPR paradox 31. The interpretation of quantum mechanics and Bell's inequalities 32. Quantum statistical mechanics and tracing over a subspace 33. Elements of quantum information and quantum computing 34. Quantum complexity and quantum chaos 35. Quantum decoherence and quantum thermalization 36. Time-independent (stationary) perturbation theory: nondegenerate, degenerate, and formal cases 37. Time dependent perturbation theory: first order 38. Time-dependent perturbation theory: second and all orders 39. Application: interaction with (classical) electromagnetic field, absorption, photoelectric and Zeeman effect 40. WKB methods and extensions: state transitions and Euclidean path integrals (instantons) 41. Variational methods 42. Atoms and molecules, orbitals and chemical bonds: Quantum chemistry 43. Nuclear liquid droplet and shell models 44. Interaction of atoms with electromagnetic radiation: transitions and lasers 45. One-dimensional scattering, transfer and S matrices 46. Three dimensional Lippmann-Schwinger equation, scattering amplitudes and cross-sections 47. Born approximation and series, S- and T-matrix 48. Partial wave expansion, phase shift method and scattering length 49. Unitarity, optics and the optical theorem 50. Low energy and bound states, analytical properties of scattering amplitudes 51. Resonances and scattering, complex k and l 52. The semiclassical: WKB and eikonal approximations for scattering 53. Inelastic scattering 54. The Dirac equation 55. Multi-particle states in atoms and condensed matter: Schrödinger vs. occupation number 56. Fock space calculation with field operators 57. The Hartree-Fock approximation and other occupation number approximations 58. Nonstandard statistics: anyons and nonabelions.
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