 Quote by stunner5000pt
Oh i have another question about this
Is this always true??
[tex] \hat{H} \Psi = E \Psi [/tex]
Here we talk about the wavefunction in general
I think this is not always true ... but i dont know understand why?? I m thinking that it ahs something to do with the time dependant case where the right is
[tex] i\hbar \frac{d}{dt} \Psi [/tex]
this term need not repsent the energy... right?
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You've already been explained the difference between a time-dependent Hamiltonian in Schroedinger picture and a time-independent one. And how that determins the time-evolution of the state vector.
[tex] \hat{H} \Psi = E \Psi [/tex]
is a spectral equation for an operator on separable Hilbert space and nothing more. It has solutions in the Hilbert space iff the spectrum of the Hamiltonian is discreet.
Daniel.
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