(a) (8 marks) Consider a classical system of N particles with Hamiltonian H(9,p) = T(p)+ V(q). The equations of motion for the system are given by ji = 1p = - The probability density for a point (9,p), in the phase space of the system, is denoted p(q, p). Explain how, for small enough N, you could construct a numerical simulation to directly calculate the temperature T of a micro-canonical system with a Hamiltonian of the form above. Give a sketch of all the necessary steps and considerations for the simulation and justify any choices you make. Write some pseudo-code as part of your explanation. (Hint: (Ex) = NkBT. (a) (8 marks) Consider a classical system of N particles with Hamiltonian H(9,p) = T(p)+ V(q). The equations of motion for the system are given by ji = 1p = - The probability density for a point (9,p), in the phase space of the system, is denoted p(q, p). Explain how, for small enough N, you could construct a numerical simulation to directly calculate the temperature T of a micro-canonical system with a Hamiltonian of the form above. Give a sketch of all the necessary steps and considerations for the simulation and justify any choices you make. Write some pseudo-code as part of your explanation. (Hint: (Ex) = NkBT