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Location of a Particle in a Box

  • #1
SOLVED
(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


[tex]
|\Psi|^2=(2/L)\sin^2{(\pi x/L)}
[/tex]
[tex]
<x> = \int^{x_0+L}_{x_0}x|\Psi|^2dx
[/tex]

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.
 
Last edited:

Answers and Replies

  • #2
Galileo
Science Advisor
Homework Helper
1,989
6
If you take the well with [itex]x_0[/itex] at the left side, then your wavefunction should also be shifted with respect to the solution for [itex]x_0=0[/itex].

You're missing [itex]x_0[/itex]in the expression for the wavefunction.
 
  • #3
right! Thanks.
 

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