Construct the classical Hamiltonian for a single particle from the corresponding Lagrangian in Cartesian, cylindrical, and spherical coordinates. Identify the canonical momenta required in each case to show that € H = 1 2m (px 2 + py 2 + pz 2 )+V(x, y, z) H = 1 2m ( prho 2 + pφ 2 rho2 + pz 2 )+V(rho,φ,z) H = 1 2m ( pr 2 + pθ 2 r 2 + pφ 2 r 2 sin2 θ )+V(r,θ,φ).