Going from the abstract state vector lψ> and the mean-value of an observable x (operator) given by:(adsbygoogle = window.adsbygoogle || []).push({});

<x> = <ψlxlψ>

I want to show how that is done in the position basis:

So I take:

<x> = <ψlxlψ>

And insert completeness in front of the state vector to get the expansion involving the wave function:

1 = ∫lx><xl (1)

But when my teacher did this he insisted on using lx'> and furthermore that you actually inserted two different operators ∫lx'><x'l and ∫lx''><x''l

both of course represent the unit operator. But I am curious as to why you need to make this primes. Why isnt (1) sufficient? Where does confusion arise and why do you need two "different" unit operators?

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# The expectation value in quantum theory

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