Syllabus for Physics 516: Electron Correlations

Spring 2010

• Lecture 1: March 22, 2010. Review of raising and lowering operators for the simple-harmonic oscillator.
• Reading:Review your old notes and texts on the raising and lowering operators for the simple harmonic oscillator.
• Lecture 2: March 24, 2010. Review of nondegenerate perturbation theory and an introduction to Wigner-Brillouin perturbation theory. (Guest lecturer Nandan Pakhira)
• Reading: Applied Quantum Mechanics 2.5, 5.4 and 16.2; Ziman, Elements of Advanced Quantum Theory, 3.1.
• Lecture 3: March 26, 2010. Degenerate Perturbation Theory I: Formalism development. (Guest lecturer Nandan Pakhira)
• Reading: Gottfried, Quantum Mechanics I, Secs 44 and 45.
• Lecture 4: March 29, 2010. Degenerate Perturbation Theory II: Summary and Atomic Fine Structure.
• Reading: Gottfried, Quantum Mechanics, Sec. 46.
• Lecture 5: March 31, 2010. Degenerate Perturbation Theory III: Hydrogen atom in an external magnetic field.
• Reading: Gottfried, Quantum Mechanics, Sec. 47.
• Lecture 6: April 7, 2010. Degenerate Perturbation Theory IV: The Stark effect and spin examples.
• Lecture 7: April 9, 2010. The time-dependent Schroedinger equation.
• Reading: Applied Quantum Mechanics, 7.1; Ziman, Elements of Advanced Quantum Mechanics, 3.2-3.4.
• Lecture 8: April 12, 2010. The interaction representation.
• Reading: Gottfried, Quantum Mechanics, Sec. 54
• Lecture 9: April 14, 2010. Cyclotron Resonance.
• Reading: Gottfried, Quantum Mechanics, Sec. 55
• Lecture 10: April 16, 2010. Properties of Time-Ordered Products.
• Lecture 11: April 19, 2010. Time-dependent perturbation theory. (Guest lecturer Joseph Wang)
• Lecture 12: April 21, 2010. Fermi's golden rule and the sudden approximation
• Reading: Applied Quantum Mechanics 7.2, 9.1-9.5
• Lecture 13: April 23, 2010. Photoproduction of Hydrogen
• Lecture 14: April 26, 2010. Fermionic creation and annihilation operators.
• Reading: Applied Quantum Mechanics, 16.1; Ziman, Elements of Advanced Quantum Theory, 2.1-2.3.
• Lecture 15: April 28, 2010. Applications of creation/annihilation operators.
• Lecture 16: April 30, 2010. The Hubbard Model
• Reading: Applied Quantum Mechanics, 20.1-20.2, 21.1-21.2.
• Lecture 17: May 3, 2010. Two-site Hubbard model solution.
• Reading: L.M. Falicov and R.A. Harris, J. Chem. Phys. 51 3153 (1969).
• Lecture 18: May 5, 2010. Nagaoka Ferromagnetism.
• Reading: H. Tasaki, Phys. Rev. B 40 9192 (1989).
• Lecture 19: May 7, 2010. Antiferromagnetism.
• Reading: E.H. Lieb, Phys. Rev. Lett. 62, 1927 (1989); J.K. Freericks and E.H. Lieb, Phys. Rev. B 51 2812 (1995).
• Lecture 20: May 10, 2010. Simulating quantum problems with ion traps.
• Reading: TBA
• Final Exam: May 12, (place to be announced).