2. Consider the raising and lowering operators of a one-dimensional harmonic oscil lator, a = ma (q+ mop) and a' = Von (q - mop), which satisfy an) = Vnln - 1), an) = Vn+ 1 + 1). (a) Show that [N, a] = -a and [N, a ] = at, where N = a a is the number operator. (c) Show that la) := e-lal /2e '10) is an eigenstate of a with eigenvalue a