Phys 500: Quantum mechanics I

Schedule and practical information

Office hours in the week of Dec 6: Wednesday 4 - 5PM. One more TBA.

Final exam: December 10, 3:30 PM - 6:00 PM, BUCH B315

Prerequisites: One of PHYS 450, PHYS 402.

Time and location: The class takes place MWF 1 PM - 2 PM in Hebb 13.

Credits: 3.

Grading: Homework: 40%, Midterm: 20%, Final: 40%.

Homework assignments:

Office hour: My office hour is Mondays and Wednesdays, 4:30-5 pm.

Past & future lectures: To browse abstracts click here.

Book: J.J. Sakurai, Modern Quantum mechanics, Addison Wesley (1994).

Additional source: C.J. Isham, Quantum Theory - Mathematical and Structural Foundations, Imperial College Press (1995).

Course outline

Phys 500 is a required course for all incoming graduate students in Physics, Medical Physics and Astrophysics. Its purpose is two-fold, namely

Material we will cover: Fundamental concepts (Pure and mixed quantum states, observables, measurement, uncertainty relations), Quantum dynamics, Theory of angular momentum, Symmetry and conservation laws, Perturbation theory, Identical particles, Quantum mechanics in medicine - medical imaging, Quantum mechanics in astrophysics, Quantum information and computation, Foundations of quantum mechanics.

Past & future lectures

Wednesday, Sep 8. First lecture. Course outline.

Friday, Sep 10.The Stern-Gerlach experiment.

Monday, Sep 13.The framework for quantum mechanics: Hilbert spaces, linear operators

Wednesday, Sep 15. Guest lecture I by Dr. Mohammad Amin, D-wave Inc., on foundations of quantum mechanics. 1. The measurement problem.

Friday, Sep 17. Guest lecture II by Dr. Mohammad Amin, D-wave Inc., on foundations of quantum mechanics. 2. Bell inequalities and Kochen-Specker theorem.

Monday, Sep 20. Back to: Measurement in quantum mechanics - the Born rule. Compatible and incompatible observables.

Wednesday, Sep 22. The uncertainty principle and the Heisenberg uncertainty relation.

Friday, Sep 24. The Schroedinger equation.

Monday, Sep 27. Unitarity. The Heisenberg picture. The Schroedinger wave equation.

Wednesday, Sep 29. The harmonic oscillator.

Friday, Oct 1. Mixed states. The no-cloning theorem. Imposibility of superluminal communication in quantum mechanics.

Monday, Oct 4. The theory of angular momentum (1).

Wednesday, Oct 6. The theory of angular momentum (2).

Friday, Oct 8. The theory of angular momentum (3). Lecture given by Dr. T.C. Wei.

Monday, Oct 18. The theory of angular momentum (4).

Wednesday, Oct 20. The theory of angular momentum (5).

Friday, Oct 22. The theory of angular momentum (6).

Monday, Oct 25. The theory of angular momentum (7).

Wednesday, Oct 27. Discrete symmetries: Parity and discrete translations.

Friday, Oct 29. Midterm exam

Monday, Nov 1. Discrete symmetries: Time reversal.

Wednesday, Nov 3. Time-independent perturbation theory, non-degenerate case. The quadratic Stark effect.

Friday, Nov 5. Time-independent perturbation theory, degenerate case. The linear Stark effect.

Monday, Nov 8. The WKB approximation.

Wednesday, Nov 10. Approximation: Variational methods.

Friday, Nov 12. Time-dependent potentials - the interaction picture. Time-dependent perturbation theory.

Monday, Nov 15. Time-dependent perturbation theory continued. Fermi's golden rule.

Wednesday, Nov 17 (2 lectures). Identical particles. The symmetrization postulate. Bosons, fermions, Pauli exclusion principle.

Wednesday, Nov 24 (2 lectures). The spin-statistics theorem. Two-electron systems. Exchange density. Ortho and para-helium.

Friday, Nov 26. Scattering theory. The Lippmann-Schwinger formalism. Methods: the Cauchy residue theorem.

Monday, Nov 29. Scattering theory continued. The Born-Oppenheimer approximation. Examples: Scattering off a Yukawa and Coulomb potential. Higher-order Born-Oppenheimer approximation.

Wednesday, Dec 1. Scattering theory continued. The optical theorem.

Friday, Dec 3. Classical and quantum cryptography. Classical: the Vernam pad, Diffie-Hellman public key exchange. Quantum: the Bennett-Brassard protocol (BB84).