Consider a quantum-mechanical particle of mass moving in a potential well,
(a) Verify that the set of normalised energy eigenfunctions are
and evaluate the corresponding energy eigenvalues .
(b) At time the wavefunction for the particle is only nonzero in the positive half of the well,
Evaluate the expectation value of the energy, first using
and secondly using
where the are the expansion coefficients in
Hence, show that