Spin

Quantum Mechanics · Part 5

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Table of Contents

  1. 1.Discovery of Spin
  2. 2.Spin Operators
  3. 3.Spin-1/2
  4. 4.Spin States
  5. 5.Pauli Matrices
  6. 6.Eigenstates of Spin Operators
  7. 7.Spin in Arbitrary Direction
  8. 8.Spin Precession
  9. 9.Spin Magnetic Moment
  10. 10.Spinors

Key Equations

$$[\hat{S}_i, \hat{S}_j] = i\hbar\epsilon_{ijk}\hat{S}_k$$
$$\det\begin{pmatrix}-\lambda & 1 \\ 1 & -\lambda\end{pmatrix} = \lambda^2 - 1 = 0$$
$$|+\rangle_y = \frac{1}{\sqrt{2}}(|\uparrow\rangle + i|\downarrow\rangle), \quad |-\rangle_y = \frac{1}{\sqrt{2}}(|\uparrow\rangle - i|\downarrow\rangle)$$
$$P(+) = |\langle +|_{\hat{n}}\psi\rangle|^2 = \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{3}{4} = 0.75$$

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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