Consider a particle of mass trapped in an infinite square well of width :
Part 1: What are the energy eigenstates?
Part 2: What is the probability of finding each eigenstate? Verify that all probabilities sum up to 1.
Part 3: Calculate the Hamiltonian .
To calculate the eigenenergies of each eigenstate of an infinite square well of width , use the formula .
We know our eigenstates are orthogonal, and a quick check shows that the wavefunction is already normalized, so we can just calculate the probabilities directly.
Our eigenvalues are the eigenenergies calculated above, so