Contenu de la matière

1. From Classical Physics to Quantum Mechanics
Particle-wave  duality,  Interference,  Wave  function,  Probability  of  presence,  Heisenbergs
Uncertainty   Principle,   the   Hamiltonian,   Schrodinger   equation,   Position   Space   and
Momentum Space, Quantum Fourier Transform.
2. Dirac Notation
Eigenvectors and eigenvalues, Adjoints and Hermitian operators, Unitary Operator, Tensor
Products, The Commutator and Anti-Commutator, Hilbert Space, braket, Observables, Ecco,
Projectors,  Solution  of  the  Schrödingers  equation  for  simple  one-dimensional  quantum
problems (the tunnel effect).
3. Postulates of Quantum Mechanics & Time Evolution
The  State  Space,  States  and  principle  of  Superposition,  Probability  Amplitudes  and
Probabilities,  Physical  Quantities  and  Operators,  Quantum  Measurement  Theory  (The
Measurement  Process,  Projective  Measurements,  POVMs...etc),  Wave  Packet  Reduction
Principle, Time Evolution of Quantum Systems, Evolution Operator and Stationary States.
4. Multipartite System and Entangled State
Pure  States,  Mixed  States  (Entangled  States),  Density  Matrices,  ,  Liouville  von  Neumann
Equation, Partial Trace and Purification, The Density Operator and the Bloch Vector, Bell
States, Open systems, Master Equation.
5. Two-State System (Qubit)
Intrinsic  Angular  Momentum  (spin),  the  Spin  Operator  and  Spin  States,  Bloch  Sphere,
Magnetic  Resonance,  Larmor  Precession,  Rabi  Oscillations,  Atom-Light  Interactions,
Jaynes-Cummings Model.