- #1
jackdamiels
- 4
- 0
Hy
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].
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].