Hi Folks,(adsbygoogle = window.adsbygoogle || []).push({});

I somehow cannot get the difference and have to admit that I am left confused.

For a probability of measuring m with the operator M on state [itex]\Psi_i[/itex]

[itex]p(m|i) = <\Psi_i| M^{+}_m M_m |\Psi_i> = <\Psi_i| M_m |\Psi_i>[/itex].

The average of an observable is defined as [itex] <O> = <\Psi_i| O |\Psi_i>[/itex].

So the measurement by M gives me a probability, the measurement with the observable an expectation value? Okay..the observables will be hermitean, the only thing I know about the measurement matrix is, that is not unitary - otherwise [itex] M^{+}_m M_m[/itex] would be equal to the unity matrix.

Is the difference that an observable doesn't change the system, but a measurement when projective projects the system into one of the states?

One last question: What is the reasoning for defining a measurement like [itex] M^{+}_m M_m [/itex] and not by M alone directly?

Thank you so much in advance..I hope the above somehow makes sense ;).

Steffen

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