Expectation value problem

1. Nov 16, 2008

kasse

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?

(Also, can sby tell me the name of the markup language I am using?)

Last edited: Nov 16, 2008
2. Nov 16, 2008

Dick

Take the expectation value of each of those three terms. You are using TeX.

3. Nov 16, 2008

HallsofIvy

Staff Emeritus
You are TOLD that <x>= 0. Put that in and your formula simplifies enormously!

4. Nov 16, 2008

kasse

If I could not simplify, could I write $$\left\langle \left\langle x \right\rangle \right\rangle = \left\langle x \right\rangle$$?

5. Nov 16, 2008

Dick

<x> is a constant (i.e. not a function). <constant>=constant. Of course those are equal.

6. Nov 16, 2008

kasse

Lol. Stupid question.