In 1912, Tetrode developed the Sackur–Tetrode equation, a quantum mechanical expression of the entropy of an ideal gas.
From Amsterdam, Tetrode corresponded with Albert Einstein, Hendrik Lorentz and Paul Ehrenfest on quantum mechanics and wrote several influential papers on quantum mechanics which were published in the German physics journal Zeitschrift für Physik.
Tetrode left for Germany in 1911 to study mathematics, physics and chemistry at the University of Leipzig, but returned to Amsterdam a year later.
In 1912, at the age of 17, he published his first research paper in the German physics journal Annalen der Physik.
He led a withdrawn life; it is said that when Einstein and Ehrenfest tried to visit him in Amsterdam, Tetrode's maid sent them away: Meneer ontvangt geen gasten ("Sir is not receiving guests").