Wave Functions of Identical Particles

Quantum mechanical probability density for two particles in a 1D well with infinite walls.

In classical statistical mechanics, identical particles are considered indistinguishable from each other (the Boltzmann-Gibbs case). Quantum mechanically, an elementary particle (meaning an irreducible finite-dimensional representation of the Poincaré group) is either a boson or a fermion, according to whether its spin (the Casimir operator of the Poincaré group) is an integer or a half-integer. Bosons and fermions cannot mix (superselection rule); wave functions representing identical bosons [fermions] must be fully symmetric [antisymmetric]. These symmetry requirements make an imprint on the probability distributions of particle groups. Statistically, bosons tend to be bunched together and fermions tend to keep away from each other, forming correlation holes. This Demonstration shows the two-particle probability distributions for the simplest possible case--particles in a square well.
comments
 
Powered by Wolfram Mathematica
Give us your feedback
Give us your feedback

Source page:




 often  occasionally  never

Note: Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific Demonstration for which you give feedback, but will not otherwise be published or distributed.
Privacy Policy »

Note: To run this Demonstration you need the free
Mathematica Player
or Mathematica 7+
Download or upgrade to Mathematica Player 7
I already have Mathematica Player or Mathematica 7+