I) A free particle of mass in one dimension has the following wavefunction:
(, ) = (^) (), ∈ ℝ.
By imposing that (, ) satisfies the free particle Schrödinger equation, deduce
the ordinary differential equation that () must satisfy. Then, solve the latter with
the initial condition (0) = 1.

ii) At time = 0, the wavefunction of a free particle of mass in 1D reads
(, 0) = sin(2)
By noticing that sin(2) is an energy eigenstate for the free particle, find the
wavefunction (, ) which solves the Schrödinger equation with the initial condition
given above. Can (, ) be normalised?