In Griffiths intro to quantum mechanics, there are a few things that I feel like he gets from nowhere, he just states it and doesn't derive it or prove it. First is equation 3.114, using opperators to get the expectation value of an observable. I get how he got the inner product from the integral, but I don't get how he got the integral in the first place. Second, in equation 3.116 which is later used in section 3.4, how does he get that definition for the standard deviation? Also, can we please not focus on the technicalities-- for example, if "derive" is not the correct term, you still know what I mean, and can you not use an entire post correcting me? I'd like to focus this thread on my two questions. Thanks!