Modern 2:Measurements and Eigenstates
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Revision as of 03:09, 27 February 2006
measurements uncertainty
We have seen that in general if N copies of a system are prepared in identical states, then the result of any measurement will have a statistical spread of values. Further, there is a fundamental connection between the uncertainty of an observable and that of its Fourier transform pair. E.g.,
It would be nice if we could expect something like
to be true, but it's not obvious.
John Baez on the time/energy uncertainty relation
One of the reasons it's not obvious is that there while there is an energy operator in QM (the Hamiltonian), there is no time operator in QM!
It turns out that from the Fourier transform ideas we've talked about you can show that:
which then gives (using Einstein's relation)
NB: that is not 
