Hilbrand Johannes Groenewold

Who is Hilbrand Johannes Groenewold?

Hilbrand Johannes Groenewold was a Dutch theoretical physicist who pioneered the largely operator-free formulation of quantum mechanics in phase space known as phase-space quantization.

He graduated from the University of Groningen, with a major in physics and minors in mathematics and mechanics in 1934. After a visit to Cambridge to interact with John von Neumann 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. In 1951, he obtained a position in Groningen in theoretical physics, first as a lecturer, then as a senior lecturer, and finally as a professor in 1955.

His seminal 1946 thesis paper firmly laid the foundations of quantum mechanics in phase space, in parallel with J. E. Moyal. This treatise was the first to achieve full understanding of the Wigner–Weyl transform as an invertible transform, rather than as an unsatisfactory quantization rule. Significantly, this work further formulated and first appreciated the all-important star-product, the cornerstone of this formulation of the theory, ironically often also associated with Moyal's name, even though it is not featured in Moyal's papers and was not fully understood by Moyal.