Representations

Quantum Mechanics · Part 1

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Table of Contents

  1. 1.From Lie Groups to Lie Algebras
  2. 2.The Angular Momentum Algebra so(3)
  3. 3.The Algebra su(2)
  4. 4.Representations of Lie Algebras
  5. 5.Important Lie Algebras in Physics
  6. 6.Exponential Map: From Algebra to Group
  7. 7.Adjoint Representation
  8. 8.Cartan Subalgebra & Roots
  9. 9.Applications in Quantum Mechanics
  10. 10.Summary

Key Equations

$$g(\epsilon) = e^{i\epsilon^a T_a} = I + i\epsilon^a T_a + O(\epsilon^2)$$
$$[\hat{J}_i, \hat{J}_j] = i\hbar\epsilon_{ijk}\hat{J}_k$$
$$[\hat{J}_i, \hat{J}_j] = i\epsilon_{ijk}\hat{J}_k$$
$$\hat{J}_\pm|j,m\rangle = \hbar\sqrt{j(j+1) - m(m\pm 1)}|j,m\pm 1\rangle$$

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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