What is the Expectation Value Problem in Quantum Mechanics?

[kasse]

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?)

 

[Dick]

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

 

[HallsofIvy]

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!

 

[kasse]

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

 

[Dick]

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

 

[kasse]

Lol. Stupid question.