Expectation value problem

Homework Statement

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?)

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Answers and Replies

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Dick
Science Advisor
Homework Helper
Take the expectation value of each of those three terms. You are using TeX.

HallsofIvy
Science Advisor
Homework Helper

Homework Statement

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

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

Dick
Science Advisor
Homework Helper
<x> is a constant (i.e. not a function). <constant>=constant. Of course those are equal.

Lol. Stupid question.