degrees of freedom of an oscillator in an Einstein solid

PhysicsGirl90

I was reading through a book on statistical physics when i came across this sentence: "An Einstein solid has two degrees of freedom for every oscillator."

How is this possible? I picture an oscillator (ex. mass on spring) to move only in one dimension, thus one degree of freedom. Where does the second degree of freedom come from?

M Quack

http://en.wikipedia.org/wiki/Einstein_solid

I am actually puzzled why there are 2 degrees of freedom, and not 3.

There are many ways to picture an oscillator.

A mass on a spring is good for 1D, but you can generalize that also to more dimensions:

Put the mass in the center of a square and attach 4 identical springs from the corners to the mass. Now the mass can oscillate in two directions. do the same with an octahedron, and the mass can oscillate in 3 directions.

A crystal corresponds best to this last case. Just instead of springs you have electric potentials (and a load of QM effects).