Historical Note

Groenewold

In 2016 it is 70 years ago that Hilbrand Johannes ("Hip") Groenewold (1910–1996) published his seminal paper "On the principles of elementary quantum mechanics", Physica 12 (1946) 405-460. In this paper, published with Groningen affiliation, Groenewold has made major contributions to the understanding of the classical-quantum correspondence. His work comprises a systematic study of how classical phase space functions can be mapped to quantum operators and vice versa. In particular he showed that in order to have an isomorphism between the algebra of phase space functions and the algebra of operators the Poisson bracket needs to be modified. Based on a new so-called star product he introduced a deformed Poisson bracket which later has been named after J. E. Moyal who developed the same theory independently at about the same time and published his work in 1949. The insufficiency of the Poisson bracket for the purpose of quantization has become the content of the well known Groenewold-van Hove theorem. Besides graduating in Groningen, Groenewold later became a professor in theoretical physics in Groningen.

Coincidentally, 2016 is also the 90th anniversary of the semi-classical approximation method called WKB by Dutch physicist H.A. Kramers among others.