In proving the Ehrenfest Theorem(adsbygoogle = window.adsbygoogle || []).push({});

This is the typical first line:

[tex]\frac{d }{dt}<O> = \frac{\partial}{\partial t} <\psi|O|\psi> = <\dot{\psi}|O|\psi> + <\psi|O|\dot{\psi}>+<\psi|\dot{O}|\psi>

[/tex]

My question is how can the exact differential

[tex] \frac{d }{dt}<O>[/tex]

be changed the partial differential

[tex] \frac{\partial}{\partial t} <\psi|O|\psi> [/tex]

in the first equality. would it not be

[tex] \frac{d }{dt}<O>=\frac{\partial}{\partial x} <\psi|O|\psi> \frac{dx}{dt}+\frac{\partial}{\partial t} <\psi|O|\psi>[/tex]

Have we assumed that [tex] \frac{dx}{dt}=0[/tex]

If so why?

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# Ehrenfest's Theorem

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