**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).

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

- To give all attending students an overview over basic concepts and modern developments in quantum mechanics and its applications.
- To prepare those students whose graduate work will involve quantum mechanics for the more advanced courses on the subject.

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.

**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).