Exercise 1: Calculate the exact form of the density of states for a typical 3D, 2D, 1D and OD system. D(E) = 2 Σ 8(E – E(k)) k -

Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. Show that the characteristic equation of the system in part (a) is 2+a+b=0.