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ehrenfest
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Homework Statement
Can someone give me a general idea (I do not need and probably will not understand the rigorous mathematics) of how you can use the propagator equation
[tex] \psi(x,t) = \int{U(x,t;x',t')\psi(x',t')dx'}[/tex],
the equation for a Gaussian wave packet,
[tex]\psi(x',0)= e^{i p_0 x'/\hbar}\frac{e^-x'^2/2\Delta^2}{(\pi\Delta^2)^{1/4}}[/tex],
to arrive at the equation [tex]\psi(x,t) = [\pi^{1/2}(\Delta+\frac{i +\hbar t}{m\Delta})]^{-1/2}
exp{\frac{-(x-p_0 t/m)^2}{2\Delta^2(1+i \hbar t/m \Delta^2}}
X exp[\frac{i p_0}{\hbar}(x - \frac{p_0 t}{2m}) ] [/tex]
Is this just a really complicated integration method? Is that a cross product or multiplcation? If it is a cross product how does come in? See Shankar 154 for more context.
Homework Equations
The Attempt at a Solution
I really do not know of any integration methods that give a cross product so I don't know. Just a general explanation would be helpfull.
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