Can expectation values be non-eigenvalues of an operator?

[cragar]

So my measurement of a quantum system is an eigenvalue of that operator.
And we are not able to predict what eigenvalue we will get, even if we knew the precise state vector before we make our measurement. But QM allows us to calculate the average of all these eigenvalues, if we made an infinite amount of measurements and then took the average. And we call this the expectation value. So the expectation value that we calculate might not even be a possible eigenvalue that we could measure?
Im just starting to learn QM. Any input will be much appreciated.

 

[jtbell]

So the expectation value that we calculate might not even be a possible eigenvalue that we could measure?

Correct.

 

[cragar]

ok thanks for your answer. Do we just define what physical observables are and then think of ways to measure these quantities that we defined. Or does nature have infinite amount of physical observables.