- Students are to be familiar with the goals and basic mathematical techniques of modern mathematical physics and, are to be prepared for advanced courses and, eventually, doing research in this area.
- Students are to understand the modern mathematical formulation of classical mechanics via Poisson geometry, as well as the modern mathematical formulation of quantum mechanic via Hilbert spaces. They understand the probabilistic framework of quantum mechanics,
- Students are to understand the theory of symmetry in classical mechanics as well as in quantum mechanics, the former via the notion of a momentum map, the latter via Wigner's Theorems.
- Students understand the phenomenon of spin via the representation theory of SU(2) and SO(3)
- Students are familiar with the basis theory of unbounded self-adjoint operators, including Stone's Theorem
- Students know the mathematically correct description of a few model Hamiltonians of quantum mechanics, such as the Hamiltonian of a free particle, the harmonic oscillator Hamiltonian, etc.
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This course is intended for students interested in the connection between mathematics and physics, and is ideal for those taking the double bachelor degree program in math and physics. It prepares, for example, for the new master course on Advanced Mathematical Physics. Following a historical introduction to mathematical physics and its goals, we discuss the modern mathematical formulation of classical mechanics as well as of quantum mechanics, paying special attention for the relationship between these theories. |
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