Proving the expectation value of any eigenvalue function

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Homework Help Overview

The discussion revolves around proving the expectation value of an eigenvalue function in quantum mechanics, specifically focusing on the calculation of the expectation value of position, , for a particle in a box potential.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to compute the expectation value using integration but encounters a result of 0 instead of the expected L/2. This leads to questions about the formulas and integration limits being used. Participants inquire about the integration limits and the size of the box in which the particle is confined.

Discussion Status

Participants are actively questioning the assumptions regarding integration limits and the physical setup of the problem. Some guidance has been offered regarding the confinement of the particle, but no consensus has been reached on the correct approach or resolution of the original poster's issue.

Contextual Notes

There is an ongoing discussion about the appropriate integration limits, which are suggested to be from -infinity to +infinity, and the size of the box, which is confirmed to be from 0 to L.

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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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