  It is shown how using the classical Hamilton-Jacobi equation one can arrive
at the time-dependent wave equation. Although the former equation was
originally used by E.Schroedinger to get the wave equation, we propose a
different approach. In the first place, we do not use the principle of least
action and, in addition, we arrive at the time-dependent equation, while
Schroedinger (in his first seminal paper) used the least action principle and
obtained the stationary wave equation. The proposed approach works for any
classical Hamilton-Jacobi equation. In addition, by introducing information
loss into the Hamilton-Jacobi equation we derive in an elementary fashion the
wave equations (ranging from the Shroedinger to Klein-Gordon, to Dirac
equations). We also apply this technique to a relativistic particle in the
gravitational field and obtain the respective wave equation. All this supports
't Hooft's proposal about a possibility of arriving at quantum description from
a classical continuum in the presence of information loss.
