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Advanced quantum mechanics
The aim of the course is to present in details some advanced theoretical tools in quantum mechanics with an emphasis on degenerate many-body systems and scattering theory.
The aim of the course is to present in details the advanced theoretical tools in quantum mechanics with an emphasis on degenerate many-body systems and scattering theory.
Syllabus
The course is divided into two parts:
a first part is devoted to the formalism of the second quantification which includes the diagonalization of quadratic Hamiltonians with applications to the Bogoliubov theory for bosons and to the BCS theory for fermions.
A second part present approximation methods for time dependent problems and discuss the resolvent operators, and the formal theory of scattering.
Prerequisites
Basic knowledge on Quantum Mechanics and Statistical Physics.
Elements on complex analysis: analytic functions and residue theorem.
Evaluation
Written exam