Angular Momentum

Quantum Mechanics · Part 4

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Table of Contents

  1. 1.Classical Definition
  2. 2.Quantum Angular Momentum Operators
  3. 3.Commutation Relations
  4. 4.Total Angular Momentum Squared
  5. 5.Eigenvalues and Quantum Numbers
  6. 6.Ladder Operators
  7. 7.Spherical Coordinates Representation
  8. 8.Spectroscopic Notation
  9. 9.Uncertainty Relations
  10. 10.Vector Model (Semiclassical Picture)

Key Equations

$$\vec{L} = \vec{r} \times \vec{p}$$
$$[\hat{L}_x, \hat{L}_y] = i\hbar\hat{L}_z$$
$$[\hat{L}^2, \hat{L}_i] = 0 \quad \text{for } i = x,y,z$$
$$\hat{L}_-|\ell,m\rangle = \hbar\sqrt{\ell(\ell+1) - m(m-1)}|\ell,m-1\rangle$$

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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