Proving the expectation value of any eigenvalue function

AI Thread Summary
The discussion centers on calculating the expectation value of a position operator for a particle in a box. The user initially finds the expectation value <x> to be 0 instead of L/2, leading to confusion about the integration process. The integration limits are clarified as from 0 to L, indicating the particle's confinement within a box of size L. The conversation emphasizes the importance of correctly applying limits in the integration to obtain the expected result. Proper understanding of the problem setup is crucial for accurate calculations.
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Homework Statement


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Homework Equations


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The Attempt at a Solution


When I take the second formula, multiply by it's conjugate and then by x and do the integral of the first formula, I get 0, and not L/2, for <x>. Am I missing a formula ?
The complex conjugate of the exponential part multiplied by the exponential part simplifies to 1, and when I do the integral I end up with 0.
 
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What are your integration limits?
 
kuruman said:
What are your integration limits?
-infinity and +infinity, as in the first formula (the orange background)
 
What is the size of the "box" the particle is in?
 
kuruman said:
What is the size of the "box" the particle is in?
L? so would it be from 0 to L ?
 
Right. The particle is confined from 0 to L.
 

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