1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quantum pendulum

  1. Oct 3, 2011 #1

    I am trying to solve problem of quantum pendulum in region of unstable equilibrium.
    I am doing it in Heiseberg interpretation of QM. The equation of motion that I am getting is
    [tex] \dot{\dot{\theta}} = \omega^2\theta [/tex],
    and the solution is in form of :

    [tex] x (t) = A\cosh(\omega t) + B\sinh (\omega t) [/tex].

    With some starting connditions I can get A i B, that is simple. But problem arose when I am computing standard deviations od for example
    [tex] (\delta x )^2 = <(x - <x>)^2 >[/tex]
    I am getting imaginary numbers, and time dependence. Time dependence is OK, because it is Heisenberg picture, but whay imagenery part in this standard deviations. State is :
    [tex] 1/{\sqrt{\sigma{sqrt{2\pi}e^{ip_0 x}e^{-\frac{(x-x_0)^2}{4\sigma^2}[/tex].
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Quantum pendulum
  1. A Pendulum (Replies: 8)

  2. Foucault Pendulum (Replies: 5)

  3. Quantum pendulum (Replies: 8)