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How is the boxed equation arrived at when looking at the step before?

I think I need clarification on a few key ideas:

in words, does < x | p | ψ > mean, "The momentum operator acting on the state vector, then projected onto the position basis"? If so, wouldn't that mean there would always be a factor of iћ since [x,p] = iћ?

Furthermore, is the reason the integral of |x'><x'| there just so you get <x'|ψ> and project ψ to the x' basis. I know it equals and identity matrix but can you do this?

Thank you

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# How is this equation for <x|P|x'> derived?

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