1. A and B are two operators, such that [A, B] = c, where c is a number. (a) Show that, e Be=B+c B] = = nc A(n-1). [Hint: First show that [A", Then show that [e4, B] = ce. (b) Use the above result to show that eA Bn eA = (B + c)" (c) Use the above result again to show that e e e-A A B B = ece (d) The above result can be used to prove (You must show) e A e(A+B) e-A= ee(A+B)