A selection principle in deformation quantization

Deformation quantization produces families of mathematically equivalent quantization procedures from which one must select the physically meaningful ones. As a selection principle we propose that the procedure must allow enough ‘observable’ energy distributions, i.e., ones for which no pure quantum state will appear with negative probability and must further have the property that for these the uncertainty in the probability distribution of the quantum states must not exceed that of the original distribution. For the simple harmonic oscillator we show that this allows only the classic Groenewold-Moyal (skew-symmetric) form.