I am reading a book in which at some point they find the time-evolved wavefunction $\phi_0(\mathbf{r},t)$ from the static $\phi_0(\mathbf{r})$.
They say that "employing the Heisenberg time evolution formalism, one can write the general result as "
$$ \phi_0(\mathbf{r},t) = e^{-3i\pi/4} \left ( \frac{m}{2\pi\hbar t}\right )^{3/2} \int d\mathbf{r}'\phi_0(\mathbf{r'}) \exp \left [ i\frac{m}{2\hbar t}(\mathbf{r} - \mathbf{r'})^2\right ].$$
Needless to say, I do not understand how this is justified. As far as I know the Heisnenberg picture time evolution just expresses the time dependence of the operator as a commutator of that operator with the Hamiltoninan...
Anyone know how to get to this expression?