In the discussion on formal aspects of quantum mechanics I have shown that the eigenfunctions to the Hamiltonian are complete, i.e., for any
(10.5) |
where
(10.6) |
We know, from the superposition principle, that
(10.7) |
so that the time dependence is completely fixed by knowing at time only! In other words if we know how the wave function at time can be written as a sum over eigenfunctions of the Hamiltonian, we can then determibe the wave function for all times.