Problems

4.1) Prove that there is a unitary operator ${\tilde {U}}(a)$, which is a function of ${\hat {p}}={\frac {\hbar }{i}}{\frac {d}{dx}}$, such that for some wavefunction $\psi (x)\!$, ${\tilde {U}}(a)\psi (x)=\psi (x+a)$.

Solution to 4.1