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andresordonez
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SOLVED
(Example 6.15 from Modern Physics 3e- Serway)
Compute the average position <x> for the particle in a box assuming it is in the ground state
<br /> |\Psi|^2=(2/L)\sin^2{(\pi x/L)}<br />
<br /> <x> = \int^{x_0+L}_{x_0}x|\Psi|^2dx<br />
<br /> <x>=x_0+L/2-\frac{L}{2\pi}\sin{\frac{2\pi x_0}{L}}<br />
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 x_0 + L/2 right?
If I take x_0=0 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 x_0 \neq 0 I get the previous answer.
(Example 6.15 from Modern Physics 3e- Serway)
Homework Statement
Compute the average position <x> for the particle in a box assuming it is in the ground state
Homework Equations
<br /> |\Psi|^2=(2/L)\sin^2{(\pi x/L)}<br />
<br /> <x> = \int^{x_0+L}_{x_0}x|\Psi|^2dx<br />
The Attempt at a Solution
<br /> <x>=x_0+L/2-\frac{L}{2\pi}\sin{\frac{2\pi x_0}{L}}<br />
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 x_0 + L/2 right?
If I take x_0=0 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 x_0 \neq 0 I get the previous answer.
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