Theoretical / proof-based
Mathematical physics · Undergraduate · Physics
Topics
Rigorous methods
- Self-adjoint operators on Hilbert spaces
- Spectral decomposition and completeness
- Distribution theory and delta functions
- Variational principles with constraints
- Asymptotic analysis of integrals (steepest descent)
Group theory
- Lie algebras from commutators
- SU(2) and angular momentum addition
- Casimir operators and irreducible reps
- Young tableaux for identical particles (intro)
- Application to crystal point groups
Advanced PDE theory
- Well-posedness and boundary value problems
- Maximum principles for elliptic equations
- Method of characteristics for hyperbolic PDEs
- Integral equations and Fredholm theory sketch
- Conformal mapping techniques
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