Syllabus
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Fundamentals of quantum mechanics.
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Hydrogen atom and H-like systems.
Hydrogenic atom energy levels and wave function.
Special hydrogenic systems: positronium; muonium; antihydrogen; muonic and hadronic atoms.
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Physical symmetries and conservation laws. Angular momentum.
Physical symmetries and conservation laws.
Quantum mechanics of angular momentum. Orbital angular momentum and spin.
Addition of the angular momenta.
Clebsch-Gordon coefficients, 3j and 6j symbols.
Wigner-Eckart theorem. Irreducible tensor operators.
Graphical representation. Angular momentum diagrams.
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Parity nonconservation in atoms: a research example.
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Identical particles.
Bosons and fermions. Symmetric and antisymmetric wave functions. Slater determinants.
Many-particle operators.
Practical application of perturbation theory and variational method.
Example: calculation of energy levels of two-electron atoms and ions (He and He-like ions).
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Second quantization
Second quantization. Example: atomic electrons. Normal form of operator product and expectation values.
Second quantization form of many-particle operators.
Example: calculation of energy levels in He and He- like ions, general case.
Wick's theorem and its practical application. Second quantization: closed shell systems.
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Self-consistent fields.
Hartree-Fock method.
Hartree-Fock equations: He-like systems and general case of
closed-shell systems.
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Scattering.
The Born approximation. Validity of the Born approximation.
The method of partial waves.
Optical theorem. Calculation of phase shifts. Scattering of two identical particles.
Solving scattering problems: examples.
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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.
Plane wave solutions of the Dirac equation.
Spherical spinors. Hydrogenic atoms: Dirac energy levels.
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Introduction to many-body perturbation theory and all-order method.
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Applications of quantum mechanics.
Magnetic effects: The Aharonov-Bohn effect.
Flux quantization in superconductors. Josephson junctions. Superconducting devices.
Masers & lasers.
Basics of quantum computation.
Superposition and entanglement.
Quantum teleportation.