  Arbitrarily small changes in the commutation relations suffice to transform
the usual singular quantum theories into regular quantum theories. This process
is an extension of canonical quantization that we call general quantization.
Here we apply general quantization to the time-independent linear harmonic
oscillator. The unstable Heisenberg group becomes the stable group SO(3). This
freezes out the zero-point energy of very soft or very hard oscillators, like
those responsible for the infrared or ultraviolet divergencies of usual field
theories, without much changing the medium oscillators. It produces pronounced
violations of equipartition and of the usual uncertainty relations for soft or
hard oscillators,and interactions between the previously uncoupled excitation
quanta of the oscillator, weakly attractive for medium quanta, strongly
repulsive for soft or hard quanta.
