Theoretical / proof-based
Physical Chemistry II · Undergraduate · Chemistry
Topics
Mathematical methods in quantum chemistry
- Linear algebra: eigenvalues, eigenvectors, and Hermitian matrices
- Variational principle and Rayleigh–Ritz method
- Perturbation theory: first-order corrections
- Angular momentum: commutation relations and ladder operators
- Spherical harmonics and hydrogen atom solutions (mathematical)
- Separation of variables in the Schrödinger equation
- Dirac notation and bra-ket formalism (introduction)
- Time-dependent perturbation theory and Fermi's golden rule (intro)
- Density matrices and mixed states (overview)
- Rigorous treatment of measurement and observables
Advanced molecular quantum mechanics
- Multi-electron atoms: Slater determinants
- Configuration interaction and correlation energy (conceptual)
- Perturbation treatment of helium atom
- Molecular orbital theory for polyatomic molecules
- Hückel theory for conjugated π systems
- Band structure of solids (introduction)
- Density functional theory: Hohenberg–Kohn theorems (overview)
- Quantum chemistry software workflows and validation
- Interpretation of computational output: orbitals, energies, frequencies
- Connecting quantum results to experimental observables
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