How to Find the Resulting Angles in a Lab-Frame Collision between Particles of Equal Mass
How to Decouple Different Particles into Linearly Independent Equations
How to Translate Cross-Sections between Center-of-Mass and Lab Frames

Create Symmetric and Antisymmetric Wave Functions for a Three-or-More-Particle Systems

In quantum physics, you can put together the symmetric and antisymmetric wave functions of a system of three or more particles from single-particle wave functions. The symmetric wave function looks like this:

image0.png

And the antisymmetric wave function looks like this:

image1.png

This asymmetric wave function goes to zero if any two single particles have the same set of quantum numbers

image2.png

How about generalizing this to systems of N particles? If you have a system of N particles, the symmetric wave function looks like this:

image3.png

And the antisymmetric wave function looks like this:

image4.png

The big news is that the antisymmetric wave function for N particles goes to zero if any two particles have the same quantum numbers

image5.png
  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
How to Find the Second-Order Corrections to Energy Levels and Wave Functions
How to Relate the Angles between Center-of-Mass and Lab Frames
How to Find the Eigenvalues and Eigenvectors for Degenerate Hamiltonians
What Happens to a Wave Function When You Swap Two Particles
How to Work with Particle Scattering and Cross-section Equations
Advertisement

Inside Dummies.com