How can I find the square of expectation value for a particle in a box?

[ghallya]

hi all

can sombody show me the way I could get
the square expectation value http://06.up.c-ar.net/03/fd4f.jpg for a particle in a box

where the answer is given to us :
http://06.up.c-ar.net/03/87d0.jpg

 

[jtbell]

$$<x^2> = \int {\psi^*(x) x^2 \psi(x)dx}$$

For the limits of integration, use the positions of the ends of the box. Some books use a box with 0 < x < L, others use -L/2 < x < +L/2, with correspondingly different wavefunctions.

 

[G.F.Again]

$$<x^2> = \int {\psi^*(x) x^2 \psi(x)dx}$$

Where psi is orthonormal.