Recent content by Homo Novus

I tried messing around with the formulas, but honestly I don't really know what I'm doing. I tried to find P(a_jp_j^2,b_jq_j^2) from P(q,p), but I don't know what to do with the d^{sN}q\,d^{sN}p left over... and then, assuming I do manage to find the correct distribution formula, I don't know...

Homework Statement For a Hamiltonian of the form H=\sum_{j=1}^m a_j p_j^2 + \sum_{j=1}^n b_j q_j^2 + H'(q_{n+1}, \dots, q_{sN}, p_{m+1}, \dots, p_{sN}) (for a system with n coordinates and m momenta, s degrees of freedom and N particles), show that \overline{a_jp_j^2}=\frac{kT}{2}, for...

Is "order" = "size"? I'm really confused... we refer to the "size" of a group as the "order"... But are they really equivalent? Can we prove that simply? Example: Say we have a group G and a subgroup H. Then take one of the cosets of H, say Hx... It has order = o(G)/o(G/H). But does this...

Hmm... The order of yH = order of G divided by n...? That, and it contains y?

Homework Statement a) Let H be a normal subgroup of G. If the index of H in G is n, show that y^n \in H for all y \in G. b) Let \varphi : G \rightarrow G' be a homomorphism and suppose that x \in G has order n. Prove that the order of \varphi(x) (in the group G') divides n. (Suggestion: Use...