Subsequent Measurements of two observables, compatible and incompatible pairs

[wavingerwin]

Homework Statement

On an arbitrary state, the observable $$\hat{A}$$ is measured returning the result $$a$$. A compatible observable $$\hat{B}$$ is then measured returning $$b$$.

If $$\hat{A}$$ is then measured again, is the same result $$a$$ obtained?
How about if $$\hat{A}$$ and $$\hat{B}$$ are not compatible observables?

Homework Equations

The Attempt at a Solution

To my understanding: for the compatible case, the second measurement of $$\hat{A}$$ would return $$a$$ since the state has collapsed to a (fully) defined state of a (complete) set of compatible observables; $$\hat{A}$$ and $$\hat{B}$$.

However, if $$\hat{A}$$ and $$\hat{B}$$ are not compatible, upon measuring $$\hat{B}$$, the information of $$\hat{A}$$ is lost, and so the second measurement of $$\hat{A}$$ can return values other than $$a$$.

Is this correct?
Thanks in advance..

 

[ideasrule]

Yes, that's correct.