S’darboux Coordinates and Wkb Approximations in Deformation Quantization

We introduce a method for calculating the joint spectra of functions which comprise a quantum integrable system under a deformation quantization star product. The main result involves a construction by formal power series in ~ of s’Darboux coordinates, a concept we introduce for the star product analogue of Darboux normal coordinates. We will find that underlying the quantum integrable system is a set of s’Darboux coordinates which in turn give rise to number operators for the system. We present an explicit correction to the lowest order Bohr-Sommerfeld or EBK quantization rule.