Mecânica Quântica II
The main objective of this course is to study applications of quantum mechanics to a variety of systems. The topics covered includes introductions to: condensed matter theory, quantum field theory and quantum information theory.
Contents:
1. Particles in a magnetic field
1.1 Gauge Fields
1.2 Landau Levels and the Quantum Hall Effect
1.3 Aharonov-Bohm Effect and Magnetic Monopoles
1.4 Spin in a Magnetic Field
2. Band Structure
2.1 Electrons Moving in One Dimension
2.2 Lattices
2.3 Tight-Binding Model
2.4 Nearly Free Electrons
2.5 Bloch's Theorem
3. Electron Dynamics in Solids
3.1 Fermi Surfaces
3.2 Dynamics of Bloch Electrons
3.3 Bloch Electrons in a Magnetic Field
4. Phonons
4.1 Quantum Vibrations
4.2 From Atoms to Fields
5. Atoms
5.1 Hydrogen
5.2 Atomic Structure
5.3 Self-Consistent Field Method
6. Atoms in Electromagnetic Fields
6.1 The Stark Effect
6.2 The Zeeman Effect
6.3 Photons
7. Quantum Foundations
7.1 Entanglement
7.2 Quantum Computation
7.3 Measurement
7.4 Open Systems
Bibliography:
The course is mainly based on the excellent notes of David Tong. David Tong: Lectures on Applications of Quantum Mechanics.
These may also be useful:
Ben Simons - Advanced Quantum Mechanics
John Preskill - Quantum Information and Computation
Other useful references:
- J.J. Sakurai, Advanced Quantum Mechanics, (Addison-Wesley, New York, 1968).
- J.J. Sakurai, Modern Quantum Mechanics, (Addison-Wesley, New York, 1994).
- D. S. Koltun e J. M. Eisenberg, quantum Mechanics of Many Degrees of Freedom, (John Wiley & Sons, New York, 1988).
- W. Greiner, Relativistic Wave Equations, (Springer, Heidelberg,1992).
- J. W. Negele e H. Orland, Quantum Many-Particle Systems, (Addison-Wesley, New York, 1988).
- C. Cohen-Tannoudji, B. Diu e F. Laloë, Quantum Mechanics, (John Wiley & Sons, New York, 1977).
- A L. Fetter e J. D. Walecka, Quantum Theory of Many Particle Systems, (McGraw-Hill, New York, 1971).
Seminars suggestions:
Hugh Everett's many worlds interpretation of quantum mechanics. (Another useful text is Quantum mechanics and reality by Bryce S. DeWitt)
BCS theory of superconductivity. The important papers are: Bound Electron Pairs in a Degenerate Fermi Gas by Leon N. Cooper, Microscopic Theory of Superconductivity by J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of Superconductivity by J. Bardeen, L. N. Cooper, and J. R. Schrieffer
Glauber's coherent states. (There's also the Nobel Lecture)
Laughlin's state of fractional Hall effect (Nobel lecture)