- #1
jewbinson
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So in the attachment, in fact (6), the formula for the propagator rectangled in red...
is the Hamiltonian ACTING on (t-t')?
is the Hamiltonian a function of (t-t')?
or should it be (this is what I think), to be more clear
U(t,t') = exp((-i/h)(t-t')H), so that when acting on a state |psi>, we have
U(t,t')|psi> = exp((-i/h)(t-t')H|psi>)
where H operates on whatever comes next. The last one makes most sense to me because U is overall an operator, so the RHS should also be an operator.
Unless it means like this:
U(t,t')|psi> = exp((-i/h)H[(t-t')|psi>]) ?
I'm really not sure which one...
is the Hamiltonian ACTING on (t-t')?
is the Hamiltonian a function of (t-t')?
or should it be (this is what I think), to be more clear
U(t,t') = exp((-i/h)(t-t')H), so that when acting on a state |psi>, we have
U(t,t')|psi> = exp((-i/h)(t-t')H|psi>)
where H operates on whatever comes next. The last one makes most sense to me because U is overall an operator, so the RHS should also be an operator.
Unless it means like this:
U(t,t')|psi> = exp((-i/h)H[(t-t')|psi>]) ?
I'm really not sure which one...
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