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Expectation value problem

  • Thread starter kasse
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  • #1
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Homework Statement



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

2. The attempt at a solution

[tex]\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[/tex]

How can I proceed here?

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

Answers and Replies

  • #2
Dick
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Take the expectation value of each of those three terms. You are using TeX.
 
  • #3
HallsofIvy
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Homework Statement



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

2. The attempt at a solution

[tex]\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[/tex]

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!
 
  • #4
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If I could not simplify, could I write [tex]\left\langle \left\langle x \right\rangle \right\rangle = \left\langle x \right\rangle [/tex]?
 
  • #5
Dick
Science Advisor
Homework Helper
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<x> is a constant (i.e. not a function). <constant>=constant. Of course those are equal.
 
  • #6
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Lol. Stupid question.
 

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