What exactly does a degree of freedom mean?

[HomogenousCow]

I have seen this word used in every context, is there a solid definition??

 

[tahayassen]

Dimension I believe.

3 degrees of freedom = 3 dimensions.

Edit: Opps. I didn't realize this was the quantum physics section. I learned about degrees of freedom from a linear algebra textbook.

 

[HomogenousCow]

Yeah well Shankar refers to spin as a degree of freedom, I believe I read somehwere that Born did thr same

 

[HomogenousCow]

Also, although not related to QM, my GR text refers to the free indices of the metric tensor as "degrees of freedom" in that section about what we can make zero with arbitrary coordinates.

 

[cattlecattle]

Yeah well Shankar refers to spin as a degree of freedom, I believe I read somehwere that Born did thr same

My understanding of degree of freedom is that any dynamic variable that can distinguish two otherwise identical particles can be thought of as a degree of freedom. For example, two electrons at the same orbital state could be further distinguished by their spin, so spin is another degree of freedom.

 

[cosmic dust]

A degree of freedom is an independent variable that describes some property of a system. The number of the collection of these independent variables that are required to completely describe a system, are called “the degrees of freedom of the system”. For each constraint that you impose the degrees of freedom reduce by one. For example, for an ideal gas in a closed container, there are the variables of “volume”, “pressure” and “temperature”, which can take any positive value. But, the three of them are not independent, because they are related by the state equation, so one variable can be expressed as a function of the other two. So the ideal gas has two degrees of freedom.