The general evolution of a ket [itex]|\psi\rangle[/itex] is according to(adsbygoogle = window.adsbygoogle || []).push({});

[itex]-i\hbar\frac{d}{dt}|\psi\rangle=H|\psi\rangle[/itex]

without specifying a representation.

From this equation, how can you simply get a equation in a certain representation [itex]F[/itex] as below:

[itex]-i\hbar\frac{\partial}{\partial t}\langle f|\psi\rangle=\langle f|H|\psi\rangle[/itex] ?

doesn't it need the validity of

[tex]\langle f|\frac{d}{dt}|\psi\rangle=\frac{∂}{∂t}\langle f|\psi\rangle[/tex]

?

does this always hold for any ket and bra in a Hilbert space and its dual space?

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# Schrodinger Equation in a representation

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