2.4.1 Only eigenvalues

1

Suppose the wave function is initially

$$\Psi = \frac{1}{\sqrt{2}} \psi_1 + \frac{1}{\sqrt{2}} \psi_2$$

where $\psi_1$ is an normalized eigenfunction of the Hamiltonian with eigenvalue $E_1$, and $\psi_2$ an eigenfunction with eigenvalue $E_2$. Suppose that the energy of the particle is now measured and found to be $E_2$. What is the wave function now, as accurately as you can tell?

2

Suppose that the energy measurement is now repeated. What is the result of that measurement?

3

Now a very accurate position measurement of the particle is made. What can you say that qualitatively will happen to the wave function?