Pauli Matrices

Quantum Mechanics · Part 5

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Table of Contents

  1. 1.Definition
  2. 2.Fundamental Properties
  3. 3.Commutation Relations
  4. 4.Anticommutation Relations
  5. 5.Products of Pauli Matrices
  6. 6.Pauli Vector
  7. 7.Exponentials of Pauli Matrices
  8. 8.Spinor Representation
  9. 9.Eigenvalues and Eigenvectors
  10. 10.Completeness

Key Equations

$$\sigma_1 = \sigma_x = \left(\begin{array}{cc}0&1\\1&0\end{array}\right)$$
$$[\sigma_i, \sigma_j] = 2i\epsilon_{ijk}\sigma_k$$
$$\sigma_y\sigma_x = -i\sigma_z, \quad \sigma_z\sigma_y = -i\sigma_x, \quad \sigma_x\sigma_z = -i\sigma_y$$
$$\chi = \left(\begin{array}{c}\alpha\\\beta\end{array}\right), \quad |\alpha|^2 + |\beta|^2 = 1$$

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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