  This note shows that Heisenberg's choice for a wave function in his original
paper on the uncertainty principle is simply a renormalized characteristic
function of a stable distribution with certain restrictions on the parameters.
Relaxing Heisenberg's restrictions leads to a more general formulation of the
uncertainty principle. This reformulation shows quantum uncertainty can exist
at a macroscopic level. These modifications also give rise to a new form of
Schrodinger's wave equation as the equation of a vibrating string. Although a
heat equation version can also be given, the latter shows the traditional
formulation of Schrodinger's equation involves a hidden Cauchy amplitude
assumption.
