Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Probability Density in Quantum Mechanics

  1. Oct 26, 2008 #1
    I am trying to calculate the variance of the position of a particle in a one dimensional box (quantum mechanics).

    I have a wavefunction, and I know the probablilty density is the integral of (the wavefunction squared) with respect to x.

    Can you please tell me how this wavefunction could be plugged in to the variance formula

    var(x) = αŦ(x - µ)²α

    (the expected value = a/2 where a is the distance between the walls)
  2. jcsd
  3. Oct 26, 2008 #2
    [tex]var(x) = <x^2> - <x>^2 = \int_{-\infty}^{\infty}\Psi^{*}(x) x^2 \Psi(x)dx - a^2/4[/tex], since <x> = a/2 and [tex]\Psi(x)[/tex] is the wavefunction.

    Edit: Sorry had a mistake.
    Last edited: Oct 26, 2008
  4. Oct 26, 2008 #3
    Perfect, thank you :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook