Suppose that you have a classical equilibrium system that is described by many continuous variables, x1 ..xM with an en...
Suppose that you have a classical equilibrium system that is described by many continuous variables, x1 XM with an energy given by: the Ci's and x0s are constants. The Ci's are all positive A) Prove that (E) regardless of the value of the constants. This result is known as the equipartition theorem - each classical quadratic degree of freedonm contributes-BT to the average thermal energy of an equilibrium system. MkBT 2 3nRT B) Use the equipartition theorem to derive the...
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4. Consider a classical particle at temperature T. Suppose the Hamilton (i.e. the total energy) function H for the particle can be written as a sum of independent quadratic terms in the variables on which H depends. That is, if H -H(31,£2... ), then Here,5 could be a position or a momentum coordinate, and the a's are constants. As an example, 2 2 Px for a ID...