First, let's write down the Hamiltonian for a free particle in one dimension:
$$
\hat{H} = -\frac{\hbar^2}{2m} \frac{d^2}{dx^2}
$$
Now, let's check if the given functions are eigenstates of the Hamiltonian:
(a) $\psi(x) = e^{ikx}$
Applying the Hamiltonian to
Show more…