# The expectation value in quantum theory

by aaaa202
Tags: expectation, quantum, theory
 P: 995 Going from the abstract state vector lψ> and the mean-value of an observable x (operator) given by: = <ψlxlψ> I want to show how that is done in the position basis: So I take: = <ψlxlψ> And insert completeness in front of the state vector to get the expansion involving the wave function: 1 = ∫lx> and furthermore that you actually inserted two different operators ∫lx'>
 P: 1,025 It may help to do this. Rather than using a continuous basis, use a discrete basis so the integral is a sum. Then write out the product of two identity operators I*I where I = (sum)|n>
 Sci Advisor HW Helper P: 11,866 We usually denote the general (abstract, assumed linear and self-adjoint) operators by capitals, A, B, C as to distinguish them from the operators for position xi and momentum pi. And then yes, using primes to distinguish between different (but unitarily equivalent) sets of x's and p's expecially when using more then one generalized completion identities. $$\langle \psi |A|\psi\rangle = \iint dx dx' \langle \psi|x\rangle \langle x|A|x' \rangle \langle x'|\psi \rangle$$

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