Exchange

Quantum Mechanics · Part 7

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Table of Contents

  1. 1.Origins of Exchange
  2. 2.Two-Electron System
  3. 3.Energy Difference
  4. 4.Physical Interpretation
  5. 5.Heisenberg Exchange Hamiltonian
  6. 6.Hund's First Rule Explained
  7. 7.Ferromagnetism
  8. 8.Molecular Bonding
  9. 9.Exchange Hole
  10. 10.Density Functional Theory

Key Equations

$$\Psi(\vec{r}_1, \vec{r}_2) = \psi(\vec{r}_1, \vec{r}_2) \chi(s_1, s_2)$$
$$\chi_T \in \{|\uparrow\uparrow\rangle, \frac{1}{\sqrt{2}}(|\uparrow\downarrow\rangle + |\downarrow\uparrow\rangle), |\downarrow\downarrow\rangle\}$$
$$J = \int\int \psi_a^*(\vec{r}_1)\psi_b^*(\vec{r}_2)\frac{e^2}{4\pi\epsilon_0|\vec{r}_1-\vec{r}_2|}\psi_b(\vec{r}_1)\psi_a(\vec{r}_2)d^3r_1d^3r_2$$
$$k_B T_C \sim J$$

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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