- #1
youngurlee
- 19
- 0
The general evolution of a ket [itex]|\psi\rangle[/itex] is according to
[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?
[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?