Find the probability of energy value after a given measurment

[Taylor_1989]

Homework Statement

I am having a issue conceptualising the problem as I believe the answer is 0.

Part c)

Homework Equations

The Attempt at a Solution

My answer is 0 and it for the following reason. A the being say time t=0 the system is in some arbitary state, then when I got to measure the particle at t=t1 the wave function collapse into the $e^{\frac{-iE_at_1}{\hbar}}|a \rangle$ so then as it in this state when I go to measure the particle again the probability of it being $E_b$ is will be 0 as the two states are orthogonal to each other, have I assume the correctly?

 

[TSny]

My answer is 0 and it for the following reason. A the being say time t=0 the system is in some arbitary state, then when I got to measure the particle at t=t1 the wave function collapse into the $e^{\frac{-iE_at_1}{\hbar}}|a \rangle$ so then as it in this state when I go to measure the particle again the probability of it being $E_b$ is will be 0 as the two states are orthogonal to each other, have I assume the correctly?

Yes, that's right.