The original name of this video lecture is: Matrices are useful in spectroscopic theory.

1. Matrices in Spectroscopic Theory
2. Coupled Harmonic Oscillators: Truncation of an Infinite Matrix
3. Building an Effective Hamiltonian
4. Atoms: 1e- and Alkali
5. Alkali and many e- atomic Spectra
6. Many e- atoms
7. How to Assign an Atomic Spectrum
8. The Born-Oppenheimer Approximation
9. The Born-Oppenheimer Approach to Transitions
10. The Born-Oppenheimer Approach to Transitions II
11. Pictures of Spectra and Notation
12. Rotational Assignment of Diatomic Electronic Spectra I
13. Laser Schemes
14. Definition of Angular Momenta
15. Matrices
16. Parity and e/f Basis
17. Hund's Cases
18. Perturbations
19. Second-order effects
20. Wigner-Eckart Theorem
21. Construction of Potential Curves by the Rydberg-Klein-Rees Method (RKR)
22. Rotation of Polyatomic Molecules I
23. Asymmetric Top
24. Pure Rotation Spectra of Polyatomic Molecules
25. Polyatomic Vibrations: Normal Mode Calculations

The goal of this course is to illustrate the spectroscopy of small molecules in the gas phase: quantum mechanical effective Hamiltonian models for rotational, vibrational, and electronic structure; transition selection rules and relative intensities; diagnostic patterns and experimental methods for the assignment of non-textbook spectra; breakdown of the Born-Oppenheimer approximation (spectroscopic perturbations); the stationary phase approximation; nondegenerate and quasidegenerate perturbation theory (van Vleck transformation); qualitative molecular orbital theory (Walsh diagrams); the notation of atomic and molecular spectroscopy.