  By using operator techniques, we solve the paraxial wave equation for a field
given by the multiplication of a Gaussian function and an entire function. The
latter possesses a unique property, being an eigenfunction of the {\it
perpendicular} Laplacian with a zero eigenvalue, a consequence of the
Cauchy-Riemann equations. We demonstrate, both theoretically and
experimentally, the inherent rotation of this field during its propagation. The
explanation for these rotations lies in the utilization of the quantum (Bohm)
potential. The simplicity of this outcome reveals promising prospects: it
enables the analytical deduction of the Fraunhofer or Fresnel diffraction
pattern. In essence, this means that obtaining the Fresnel or Fourier transform
of a function satisfying the Cauchy-Riemann equations becomes a straightforward
task.
