  The Schroedinger- and Klein-Gordon equations are directly derived from
classical Lagrangians. The only inputs are given by the discreteness of energy
(E=hbar.w) and momentum (p=hbar.k), respectively, as well as the assumed
existence of a space-pervading field of "zero-point energy" (E_0=hbar.w/2 per
spatial dimension) associated to each particle of energy E. The latter leads to
an additional kinetic energy term in the classical Lagrangian, which alone
suffices to pass from classical to quantum mechanics. Moreover, Heisenberg's
uncertainty relations are also derived within this framework, i.e., without
referring to quantum mechanical or other complex-numbered functions.
