Expectation value problem

Thread Starter

boks

Joined Oct 10, 2008
218
1. The problem statement, all variables and given/known data

Calculate \[\Delta x = \sqrt{\left\langle(x - \left\langle x \right\rangle )^2 \right\rangle}\] if \[\left\langle x \right\rangle = 0 \] and \[\left\langle x^2 \right\rangle = a^2(\frac{\pi - 6}{12 \pi^2})\]

2. The attempt at a solution

\[\left\langle(x - \left\langle x \right\rangle )^2 \right\rangle = \left\langle x^2 - 2x \left\langle x \right\rangle + \left\langle x \right\rangle ^2 \right\rangle\]

How can I proceed here?
 

steveb

Joined Jul 3, 2008
2,431
1. The problem statement, all variables and given/known data

Calculate \[\Delta x = \sqrt{\left\langle(x - \left\langle x \right\rangle )^2 \right\rangle}\] if \[\left\langle x \right\rangle = 0 \] and \[\left\langle x^2 \right\rangle = a^2(\frac{\pi - 6}{12 \pi^2})\]

2. The attempt at a solution

\[\left\langle(x - \left\langle x \right\rangle )^2 \right\rangle = \left\langle x^2 - 2x \left\langle x \right\rangle + \left\langle x \right\rangle ^2 \right\rangle\]

How can I proceed here?
Wouldn't the next logical step be to take advantage of the fact that \[\left\langle x \right\rangle = 0 \] ?

The problem looks a whole lot simpler once you do that. :)
 
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