Question

How many degrees of freedom does a system have if there are N particles that can...

How many degrees of freedom does a system have if there are N particles that can move in 3 dimensions and each particle has a spin that can point either up or down? How many total spin states are available to this system?

Homework Answers

Answer #1

Each particle has 3 translational degrees of freedom.

So N particles has 3N translational degrees of freedom. This can be considered as 3N particles confined in one dimension.

Each particle has two spin degrees of freedom. So total degrees of freedom is 3N*2

Suppose we have two particle, how many ways can this two-particle distributed in 2 energy state is 4 (22). If we have three particles we can do it in 8 (= 2 3) ways.

So 3N particles can be distributed in 2 3N ways in two states of spin.

Here we assumed no interaction between the spins

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