Hi, Please refer to this book (in google archive), and go to section 7.7 (page 85). http://books.google.com/books?id=MnY1jUP9nlIC&pg=PR11&lpg=PR11&dq=%22time+dependent+expectation+values%22+%22quantum%22+%22harmonic+oscillator%22+-abstract+-annihilation&source=bl&ots=cSOfuC8k9y&sig=Wdc327g7A5yA6n61L0ZLlKmu-Yk&hl=ar&sa=X&ei=dK-AUOagGueF4ASoxoGgCg&ved=0CFcQ6AEwCA#v=onepage&q&f=false I understand Ehrenfest theorem very well, but what the author does when he solved for the time-dependent expectation value of x, x^2, etc is strange. I cannot really understand what he is doing. If someone wants to help, you may consider x^2 case (the book solves all the cases so please refer to it). Thanks in advance!