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This is probably a very easy questions about the one-dimension momentum operator derivation. So you take the d<x>/dt to find the "velocity" of the expectation value. At one point in the derivation early on, you bring in the d/dt into the integral of the expectation value. The book I'm going off of just basically takes the x out of the derivative because I'm guessing it isn't a function of time.

My question is, how do I know it's not a function of time? When I was trying to do the derivation alone before I looked at the book I used the chain rule here, and obviously made a mess. How do you know that x isn't really x(t)? I dunno I used to make this mistake in classical mechanics, and always assume x or theta wasn't a function of time, so I wouldn't treat them accordingly when doing derivatives. How do I know this x is different?

If anyone would like to help me out here, but wants to see more lines of the derivation I could post them. I just didn't take the time now because I again forget all the latex I learned from the last time I used it, probably a year ago. Just let me know if it would help you out.

Thanks anyone for your time.

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# Momentum Operator Derivation Questions

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