General Angular

Quantum Mechanics · Part 5

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Table of Contents

  1. 1.Abstract Definition
  2. 2.General Eigenvalue Problem
  3. 3.Ladder Operators
  4. 4.Action on States
  5. 5.Matrix Representation
  6. 6.Orbital vs Spin
  7. 7.Selection Rules
  8. 8.Rotations

Key Equations

$$[\hat{J}_i, \hat{J}_j] = i\hbar\epsilon_{ijk}\hat{J}_k$$
$$\hat{J}_z|j,m\rangle = \hbar m|j,m\rangle$$
$$[\hat{J}_z, \hat{J}_\pm] = \pm\hbar\hat{J}_\pm, \quad [\hat{J}_+, \hat{J}_-] = 2\hbar\hat{J}_z, \quad [\hat{J}^2, \hat{J}_\pm] = 0$$
$$J_z = \hbar\left(\begin{array}{ccc}1&0&0\\0&0&0\\0&0&-1\end{array}\right)$$

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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