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

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SUMMARY

The discussion focuses on calculating the square of the expectation value for a particle in a box, specifically using the formula = ∫ ψ*(x) x^2 ψ(x) dx. It highlights the importance of defining the limits of integration based on the box's dimensions, either 0 < x < L or -L/2 < x < +L/2, which correspond to different wavefunctions. The wavefunction ψ is noted to be orthonormal, which is crucial for accurate calculations.

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ghallya
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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
 
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[tex]<x^2> = \int {\psi^*(x) x^2 \psi(x)dx}[/tex]

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.
 
jtbell said:
[tex]<x^2> = \int {\psi^*(x) x^2 \psi(x)dx}[/tex]
Where psi is orthonormal.
 

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