In particular, he authored an important treatise on spherical harmonics and Legendre functions (Handbuch der Kugelfunctionen).

In 1840 Heine returned to Berlin, where he studied mathematics under Peter Gustav Lejeune Dirichlet, while also attending classes of Jakob Steiner and Johann Franz Encke.

In 1842 he was awarded a PhD by the University of Berlin for a thesis on differential equations submitted with Enno Dirksen and Martin Ohm as advisors.

In Königsberg Heine got in contact with fellow students Gustav Kirchhoff and Philipp Ludwig von Seidel.

In 1856 Heine moved as a full professor to the University of Halle, where he remained for the rest of his life.