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Jul 21 at 1:38 comment added James If we specify $\Psi$ over all space and all time past and future, then yes, arbitrarily specified initial $\Psi(x,t)$ will most likely fail the TDSE. But if we only specify $\Psi$ over all space but at current time only, then ask TDSE to extrapolate the function for all future times, then automatically the time evolution results will satisfy the TDSE. i.e. the only question is whether the initial condition we specified can be prepared.
Oct 1, 2019 at 3:15 vote accept Jack Ceroni
Oct 1, 2019 at 3:13 answer added creillyucla timeline score: 2
Oct 1, 2019 at 3:11 comment added Noiralef The Schroedinger equation is $i\hbar\partial_t |\psi(t)\rangle = H|\psi(t)\rangle$. It describes the time evolution of the state. It does not restrict the state at a single point in time, $\psi(0)\rangle$, in any way -- what do you mean by "unphysical state"?
Oct 1, 2019 at 2:58 history edited Jack Ceroni CC BY-SA 4.0
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Oct 1, 2019 at 2:52 history asked Jack Ceroni CC BY-SA 4.0