Symmetrization

Quantum Mechanics · Part 7

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Table of Contents

  1. 1.The Problem of Indistinguishability
  2. 2.Two-Particle States
  3. 3.Exchange Operator
  4. 4.Symmetric and Antisymmetric States
  5. 5.The Symmetrization Postulate
  6. 6.Constructing Symmetric States
  7. 7.Constructing Antisymmetric States
  8. 8.N-Particle Generalization
  9. 9.Slater Determinant
  10. 10.Physical Consequences

Key Equations

$$|\psi\rangle = |\psi_a(1)\rangle \otimes |\psi_b(2)\rangle$$
$$\psi_S(\vec{r}_1, \vec{r}_2) = \psi_S(\vec{r}_2, \vec{r}_1)$$
$$|\psi_S\rangle = |a\rangle_1|a\rangle_2$$
$$|\psi_S\rangle = \frac{1}{\sqrt{N!}}\sum_{P} |a\rangle_{P(1)}|b\rangle_{P(2)}\cdots|z\rangle_{P(N)}$$

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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