Expectation value of position of wavepacket

by Werbel22
Tags: expectation, position, wavepacket
Werbel22 is offline
Mar23-10, 04:18 AM
P: 8
Hello, this is just a general question, how is <x^2> evaluated, if

<x> = triple integral of psi*(r,t).x.psi(r,t).dr (this is the expectation value of position of wavepacket)

Is it possible to square a triple integral? Is <x^2> the same as <x>^2 ?

I'm only wondering how the squared works in this situation, I would understand how to use <x> if the square wasn't there.

Thank you!
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
nickjer is offline
Mar23-10, 09:37 AM
P: 676
You cannot square the integral. The way it is written is (in 1 dimension):

[tex]\left<x^2\right> = \int \psi(x)^{\dagger}x^2\psi(x) dx[/tex]

It will be different in most cases from <x>^2. For example,

[tex]\int x^2 dx = \tfrac13 x^3 \neq \left(\int x dx\right)^2 = \tfrac14 x^4[/tex]

So you are unable to take the square outside of the integral.
Werbel22 is offline
Mar23-10, 11:23 PM
P: 8
Got it, thank you very much!

Register to reply

Related Discussions
The Expectation of X and the Expectation of X squared (discrete math) Calculus & Beyond Homework 2
Why wavepacket? Quantum Physics 6
Time derivate of the Expectation value for the product of position and momentum ops Quantum Physics 2
Position expectation value of a particle in a box Advanced Physics Homework 5
expectation values in momentum/position space? Quantum Physics 0