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(Example 6.15 from Modern Physics 3e- Serway)

1. The problem statement, all variables and given/known data

Compute the average position <x> for the particle in a box assuming it is in the ground state

2. Relevant equations

[tex]

|\Psi|^2=(2/L)\sin^2{(\pi x/L)}

[/tex]

[tex]

<x> = \int^{x_0+L}_{x_0}x|\Psi|^2dx

[/tex]

3. The attempt at a solution

[tex]

<x>=x_0+L/2-\frac{L}{2\pi}\sin{\frac{2\pi x_0}{L}}

[/tex]

I'm pretty sure this is the answer, however, I don't understand why I get that last term, I mean, the average position should be [tex] x_0 + L/2 [/tex] right?

If I take [tex]x_0=0[/tex] then the answer is what I was hoping for (Indeed this is the original procedure in the book), but in the more general expression with [tex] x_0 \neq 0 [/tex] I get the previous answer.

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# Homework Help: Location of a Particle in a Box

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