- #1

dRic2

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suppose I have an operator ##A## and an eigenfunction ##\psi = c_1 \psi_1 + c_2 \psi_2## for ##A## so that

$$ A\psi = a\psi$$ The expected value is

##\langle A \rangle = \langle \psi|A|\psi \rangle = a##

After a measurement ##a## can be ##a_1## or ##a_2## and the probability of a particular outcome is ##|c_i|^2##.

Let's say the outcome of my measurement is ##a_1##. Now I'm certain about this, right? The uncertainty of ##a_1## is now ##0## because I measured it and so I forced the particle to be in the state with eigenvalue ##a_1##.

Now suppose I take the operator ##B##

__incompatible__with ##A## and I try to evaluate:

$$\langle B \rangle = \langle \psi_1|B|\psi_1 \rangle = b$$

(because I know that after my measurement the particle is in the state ##\psi_1##).

__This last operation is totally meaningless__because, since ##a_1## is certain, the uncertainty of ##b## should be ##\infty## so, even if I can calculate an "expected value" for ##B## it has no physical significance because its uncertainty is ##\infty## , right ?

Is it correct?

Thanks

Ric