In Griffiths book, he says (a+ + a-)2 = a+2 + a-2 + a+a- + a-a+. Why can you NOT do the same thing for a+2 = (-ip+mωx)2 ?! When I do this to find the 2nd excited state of SHO, it gives me wrong answer. I actually have to apply a+ two times to ψ0 in order to get ψ2. It is ridiculous that Griffiths does not mention at all why certain operators can be squared but others cannot. Could someone please elaborate on the difference between these two cases?