Deriving the time-independent Schrödinger equation

[coki2000]

How can time-independent schrödinger equation be proven? Do you know any source which explains it clearly? Thanks for replies.

 

[dextercioby]

The so-called time independent SE is nothing else but the spectral equation for the Hamilton operator. One postulates the general Schroedinger equation (alternatively one postulates a unitary evolution of physical states and then derives the SE by considering the self-adj generator of the symmetry) from which then, in the very fortunate case in which the Hamiltonian is time-independent, one can separate the time-component of the state vector completely and end up with the spectral equation of the Hamiltonian. Solving it would normally provide us the the basis for the vector space of possible physical states of the system. And the possible values for the energy of the system.

 

[tom.stoer]

How can time-independent schrödinger equation be proven? Do you know any source which explains it clearly? Thanks for replies.

You can't prove this equation (you can't prove F=m*a, either), but you can motivate it.