A general expression for the classical Hamiltonian is:

H = α p_i² + H€²

where p_i is the momentum along one dimension for particle i, α is a constant, and H€² are the remaining terms in the Hamiltonian. Substituting this into the equipartition theorem yields:

a. Starting with this expression, isolate the term involving p_i and determine its contribution to q.

b. Given that the average energy, Œ©ÎµŒª, is related to the partition function as follows:

Evaluate the expression for the contribution from p_i. Is your result consistent with the equipartition theorem?

B(p} +H')dpNdxN 3N (e) %3!