Light quanta are treated by wave mechanics by analogy with electrons. It is shown that their wave equation is the ordinary optical wave equation. Heisenberg's principle of indeterminateness becomes a description of diffraction. In problems in which localization of quanta is found experimentally, wave packets are to be set up; these are applied to the experiments of Bothe and Geiger, and of Compton. The paths of quanta coincide with the rays of geometrical optics, with a deviation of the error in geometrical optics; by the principle of indeterminateness, more accurate laws for the paths are neither necessary nor possible.
Via Nelson's stochastic mechanics, a method for the solution of the hydrodynamical version of the logarithmic nonlinear Schr\"odinger equation (LNLSE), with a time-dependent forced-harmonic-oscillator potential, is presented. Based on a new interpretation of the interplay between dispersion and nonlinearity, a revealing general spreading-wave-packet solution is found. The complete stochastic process associated with the LNLSE is also derived and decomposed into underlying processes of independent nature (classical and quantum). Physical consequences and conditions which allow the existence of solitonlike (nonspreading) solutions are described: Among them, it is found that the zero-point energy is given by ${\ensuremath{\epsilon}}_{0}$=\ensuremath{\Elzxh}${\ensuremath{\Omega}}_{0}$/2, where ${\ensuremath{\Omega}}_{0}$=\ensuremath{\lambda}/2+[(\ensuremath{\lambda}/2)+${\ensuremath{\omega}}_{0}^{2}$]
1/2 with ${\ensuremath{\omega}}_{0}$ and \ensuremath{\lambda} being the harmonic frequency and the nonlinearity strength, respectively.