1. Historical survey of quantum mechanics: de Broglie waves, Heisenberg's matrices of infinite order, Schrödinger wave equation, Born's interpretation of wave, Born's postulates, Copenhagen interpretation 2. Quantum mechanics: definition, physics view of quantum mechanics postulates 3. Experiment in quantum mechanics: Heisenberg uncertainty principle, measuring, difference from classical mechanics 4. Non-locality, decoherence, non-determinism, paradoxes of quantum mechanics (EPR and Bell's inequalities, Schrödinger's cat) 5. Finite dimensional complex Hilbert space - 1st part: Dirac's notation, linear dependence, orthonormal basis, Gram - Schmidt orthogonal process, inner product, vector norm, metric 6. Finite dimensional complex Hilbert space - 2nd part: operators (normal, self-adjoint, positive definite, positive semi-definite), unitary mapping 7. Finite dimensional complex Hilbert space - 3rd part: Hermitian operator, commutator, anticommutator, eigenvectors and eigenvalues of an operator, tensor product of vectors and operators, tensor product properties 8. The density operator 9. Postulates of quantum mechanics using density operator and vectors in Hilbert space 10. Quantum bit - 1st part: Stern - Gerlach experiment, mathematical model, geometrical visualization, non-cloning theorem, physical realization 11. Quantum bit - 2nd part: quantum bit transformation, state of quantum bit (pure, mixed, entanglement), teleportation, Superdense coding 12. Quantum bit - 3rd part: estimation and discrimination of quantum states
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