  It is shown that the Schrodinger equation for a large family of pairs of
two-dimensional quantum potentials possess wavefuctions for which the amplitude
and the phase are interchangeable, producing two different solutions which are
dual to each other. This is a property of solutions with vanishing Bohm
potential. These solutions can be extended to three-dimensional systems. We
explicitly calculate dual solutions for physical systems, such as the repulsive
harmonic oscillator and the two-dimensional hydrogen atom. These dual
wavefunctions are also solutions of an analogue optical system in the eikonal
limit. In this case, the potential is related to the refractive index, allowing
the study of this two-dimensional dual wavefunction solutions with an optical
(analogue) system.
