Group Theory

Quantum Mechanics · Part 1

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Table of Contents

  1. 1.What is a Group?
  2. 2.Examples of Groups
  3. 3.Continuous vs. Discrete Groups
  4. 4.Representations
  5. 5.Generators and Lie Algebras
  6. 6.Schur's Lemma
  7. 7.Applications in QM
  8. 8.Important Groups in Quantum Mechanics
  9. 9.Summary
  10. 10.Physical Interpretation

Key Equations

$$SO(3) = \{R \in \mathbb{R}^{3\times 3} : R^T R = I, \det R = 1\}$$
$$T(\vec{a})\psi(\vec{r}) = \psi(\vec{r} - \vec{a})$$
$$U(1) = \{e^{i\theta} : \theta \in [0, 2\pi)\}$$
$$\rho: G \to GL(V)$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Mechanics course on CoursesHub.World. Master quantum mechanics from mathematical foundations to advanced topics. Covers Hilbert spaces, wave functions, angular momentum, perturbation theory, scattering, and path integrals with 450+ pages ...

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