Skip to main content
Physics LibreTexts

7: Multiple Particles

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    • 7.1: Identical Particles
      The notion of particles being indistinguishable from each other takes on new meaning when considering the quantum state of a system of these particles.
    • 7.2: Exclusion Principle
      We look at the principle credited to Wolfgang Pauli, how it relates to spin, and its consequences for multiple particles in bound states.
    • 7.3: Periodic Table of Elements
      We extend some of our results from the hydrogen atom, and add-in the exclusion principle to give a basic foundation for the principles of chemistry.
    • 7.4: Boltzmann Distribution
      Systems of many particles at a given temperature will distribute the energy amongst the energy levels available to the particles in different ways, based upon the types of particles (fermions or bosons), and whether or not they are distinguishable.
    • 7.5: Quantum Distributions
      We already know that identical particles that are in close enough proximity produce non-classical results, so it should not be surprising that the classical Boltzmann distribution fails to correctly account for the statistical distribution of energy under these conditions.
    • 7.6: Model Examples
      We look at a couple examples of models that use the formalism we have built around quantum distributions.

    7: Multiple Particles is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Tom Weideman directly on the LibreTexts platform.

    • Was this article helpful?