# Electron correlation vs electron exchange

• I
Rzbs
TL;DR Summary
What is difference between electron correlation and electron exchange?
What is the difference between electron correlation and electron exchange?
Which of them is due to the spin of electrons and which is due to charge of electrons?

Gold Member
All of this can be easily understood mathematically using the so-called correlation functions, but I'll try to explain with words.

First, consider two neutral (non interacting) classical particles. In this case the two particles basically ignore each others so the evolution in time of each particle is totally independent (uncorrelated) of the other.

Now let's add a little bit of quantum mechanics: suppose the two particles are now indistinguishable. This is a purely quantum mechanical phenomenon and it changes the system. The two particles are still non-interacting (so their time evolution is still independent from each other) but now you get all the quantum mechanical effects that follow from indistinguishability (ex. exclusion principle). This is roughly the electron-exchange.

Finally suppose the particles are charged. Now the evolution of one particle is dependent of the other in a pretty complicated way and we say the particles are correlated.

Schematically you can think it this way:
classical view + exchange + correlation = real qm description.

In some cases the exchange term and the correlation terms are unified into the so-called exchange-correlation term.

• etotheipi and Rzbs
Rzbs
Thanks

• 