In 1946, Hip Groenewold demonstrated that a general systematic correspondence between quantum commutators and Poisson brackets could not hold consistently.
After a visit to Cambridge to interact with John von Neumann (1934-5) on the links between classical and quantum mechanics, and a checkered career working with Frits Zernike in Groningen, then Leiden, the Hague, De Bilt, and several addresses in the North of Holland during World War II, he earned his Ph.D. degree in 1946, under the tutelage of Léon Rosenfeld at Utrecht University.
For the archetypal example, one may well consider Groenewold's original ★"Moyal–Weyl" ★-product.