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> eigenvalues $$\alpha_1,\alpha_2$$. Operator $$\hat{B}$$ has also two

> normalized eigenstates $$\phi_1,\phi_2$$ with eigenvalues

> $$\beta_1,\beta_2$$. Eigenstates satisfy:

> $$\psi_1=(\phi_1+2\phi_2)/\sqrt{5}$$

> $$\psi_2=(2\phi_1-\phi_2)/\sqrt{5}$$

>

> We measure the quantity $$A$$ and we get the value $$\alpha_1$$. What's

> the state of the system after the measurement?

>

> What are the possible outcomes after the measurement of the quantity

> $$B$$? What is the probability of getting each one of them?

To begin with, I assume that, since the eigenfunction corresponding to the measured eigenvalue is $\psi_1$, this is also the state of the system after the measurement.

As for the possible outcomes of the measurement of $B$, I'm thinking of expressing $\psi_1,\psi_2$ as functions of $\phi_1,\phi_2$ and using them as eigenstates of $B$. Any help?