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Up: 10. Time dependent wave
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In the discussion on formal aspects of quantum mechanics I have shown
that the eigenfunctions to the Hamiltonian are complete, i.e., for any
(x, t)
(x, t) = cn(t) (x), |
(10.5) |
where
We know, from the superposition principle, that
(x, t) = cn(0)e-iEt/ (x), |
(10.7) |
so that the time dependence is completely fixed by knowing c(0) at
time t = 0 only! In other words if we know how the wave function at
time t = 0 can be written as a sum over eigenfunctions of the
Hamiltonian, we can then determibe the wave function for all times.