  The paraxial approximation to the scalar Helmholtz equation is shown to be
equivalent to the Schr\"odinger equation for a quantum harmonic oscillator.
This equivalence maps the Gouy-phase of classical wave optics onto the time
coordinate of the quantum harmonic oscillator and also helps us understand the
qualitative behavior of the field and intensity distributions of focused
optical beams in terms of the amplitude and probability distributions of
quantum harmonic oscillators and vice versa.
