Lectures related to Molecular Vibrations & Normal Modes

Explores k-fold degenerate sets of eigenfunctions and their basis for irreducible representations.

Covers the concept of eigenfunctions of H as bases for irreducible representations and integrals.

Explores group representations using matrices, discussing reducible vs. irreducible representations and the Great Orthogonality Theorem.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores the solution of the Schrödinger equation for many-electron systems using basis sets and the concept of basis functions.

Covers the summary and rules related to bases of representations in Symmetry 2021.

Explores representations of C3v symmetry, character tables, Mulliken symbols, and group theory applications in eigenfunctions.

Covers the fundamentals of spectroscopy, including tools, color, Doppler effect, and molecular behavior.

Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Explores molecular quantum optomechanics, discussing light-matter interactions in molecular vibrations and the quantization of these vibrations.

Covers the fundamentals of spectroscopy, including selection rules and transitions.

Covers molecular orbital theory, SALCs, and molecular vibrations.

Covers the exact analytical solution methods for linear ODEs using matrices and eigenvalues.

Covers complex reactions, rate laws, differential equations, and steady-state approximation for parallel reactions.

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.