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Identical coursesAdvanced Quantum Mechanics (B-KUL-G0S83A)
Cannot be taken as part of an examination contractAims
Students acquire a more deeper knowledge on the nature and the power of quantum mechanics. In particular they know how to apply perturbation theory, to employ scattering theory and to apply symmetry arguments. Students also get in touch with more modern aspects of quantum mechanics like in questions about entanglement, non-localities and the measurement problem.
Previous knowledge
Students have followed courses in General Physics, and they also have successfully finished a basic course in quantum mechanics.
Order of Enrolment
This course unit is a prerequisite for taking the following course units:
G0S91A : Advanced Nuclear Physics
Identical courses
This course is identical to the following courses:
G0S84A : Gevorderde kwantummechanica
Is included in these courses of study
Activities
6 ects. Advanced Quantum Mechanics (B-KUL-G0S83a)
Content
1. Reminders: quantumformalism for closed systems, two-slit experiment. Schroedinger equation with spin (Pauli and Dirac equations) - Stern-Gerlach experiment. Quantumstatistics.
2. Complements:
- Time-dependent Hamiltonian, quantum protocol and control;
- Time-dependent perturbation theory (Dyson method);
- Scattering theory (Landauer-Buttiker formula);
- Symmetry considerations (the hydrogen atom revisited);
- Approximations (semi-classical analysis, WKBJ-method, Born-Oppenheimer approximation).
3. Modern developments:
- Open systems, dissipative evolutions, decoherence, Caldeira-Leggett model. Weak coupling (Fermi-Golden rule), Lindblad equation;
- Quantum nature: superposition, entanglement, tunneling, nonlocality;
- Quantum optics. Jaynes-Cummings model, Rabi oscillations, coherent states, squeezing, manipulations of individual atoms;
- Quantum system theory. Positive-operator valued measure, quantum computing and algorithms, compression and capacity.
Depending on available time and taking into account the possible overlap with other courses:
- Introduction to path-integrals (example: Ahoronov-Bohm effect);
- From Einstein-Podolsky-Rosen experiments to Bell inequalities and the Kochen-Specker No-Go Theorems;
- Schroedinger’s cat and possible solutions of the measurement problem.
Course material
“Quantum Mechanics” by Bransden&Joaquin ;
"Quantum computing and quantum information" by Nielsen&Chuang;
“Quantum Mechanics, A Modern Development” by L.E. Ballentine
And lecture notes.
Format: more information
Basic lectures and exercises for optimal interaction.