Lectures

Lectures 1,2. (09/04, 09/09)

Syllabus and general course information.
Applications of quantum mechanics: basics of quantum computation. Review topics: superposition and entanglement.
Applications of quantum mechanics: quantum teleportation.
Quiz #1 (Topics: fundamentals of quantum mechanics, hydrogen-like systems,
practical addition of the angular momenta, electric-dipole transitions.)

Lecture 3. (09/11)

Review: postulates of quantum mechanics, hydrogenic systems, basics of angular momentum addition,
atomic energy levels and spectroscopic notations.
Electric-dipole operator and corresponding transition selection rules.

Lecture 4. (09/18)

How does one solve the Schrödinger equation? Example: hydrogen-like atom.
Special hydrogenic systems: positronium; muonium; antihydrogen; muonic and hadronic atoms.

Lecture 5. (09/23)

Physical symmetries and conservation laws. Orbital angular momentum.
Quantum mechanics of the angular momentum. Spin.

Lecture 6. (09/25)

Addition of the angular momenta. Clebsch-Gordon coefficients, 3j and 6j symbols.
Graphical representation.
Wigner-Eckart theorem. Irreducible tensor operators.

Lecture 7. (09/30)

Graphical representation. Angular momentum diagrams.

Lectures 8, 9. (10/02, 10/07)

Research example: parity nonconservation in atoms.
Topics: conservation laws, perturbation theory, angular momentum addition, reduced matrix elements,
Wigner-Eckart theorem, hyperfine states, summation over magnetic moments: use of angular diagrams.
RESEARCH PROJECT #1.

Lectures 10 and 11. (10/9, 10/16)

Identical particles. Bosons and fermions. Quarks and colors. Symmetric and antisymmetric wave functions.
Slater determinants. Many-particle operators. Rules for calculation of matrix elements of one-particle and two-particle operators.
Example: energy levels of two-electron atoms and ions (He and He-like ions).
Practical application of perturbation theory and variational method. Quiz #2

Lectures 12 and 13. (10/17, 10/21)

Second quantization (example: atomic electrons). Normal form of operator product.
Many-particle operators in second quantizations. Example: Coulomb two-particle matrix element.
Application: calculation of energy levels in He and He-like ions (general case: LS coupled states).

10/23 Midterm exam.

Lecture 14. (10/30)

Second quantization. Normal form of operator product and expectation values. Contractions.
Wick's theorem. Second quantization: closed shell systems. RESEARCH PROJECT #2

Lectures 15-17. (10/31, 11/4, 11/6)

Self-consistent fields.
Hartree-Fock equations: He-like systems. Hartree-Fock equations: closed-shell systems.

Lectures 18-19. (11/11, 11/13)

Scattering. Differential cross section. The Born approximation. Validity of the Born approximation.
Solving scattering problems: examples. QUIZ #3

Lectures 20-21. (11/20, 11/21)

The method of partial waves. Optical theorem. Calculation of phase shifts. Examples.

Lecture 22. (11/25)

Scattering of two identical particles.
Relativistic Quantum Mechanics. Klein-Gordon equation and the interpretation of the Klein-Gordon equation.
The Dirac equation, Dirac representation for the matrices a and b, covariant form of the Dirac equation.

Lecture 23. (12/2)

Plane wave solutions of the Dirac equation. Spherical spinors.
Hydrogen-like systems … again (relativistic version). Dirac energy levels.

Lecture 24. (12/4)

Introduction to many-body perturbation theory and all-order methods. Example: alkali-metal atoms.
A particle in electromagnetic field. Magnetic effects: The Aharonov-Bohn effect.

Lectures 24-25. (12/4, 12/9)

Applications of quantum mechanics. Magnetic effects: The Aharonov-Bohn effect.
Flux quantization in superconductors. Josephson junctions. Superconducting devices.
Masers & lasers.