Heller is known for his work on time-dependent quantum mechanics, and also for producing digital art based on the results of his numerical calculations.

In 1981, Heller took a sabbatical at Los Alamos National Laboratory and then stayed on as a staff scientist until 1984 when he accepted a faculty position in Chemistry at the University of Washington.

In 1998, Heller stepped down as ITAMP director to assume a joint appointment to the Harvard University Chemistry department.

Heller has received the American Chemical Society Award in Theoretical Chemistry (2005), the Astor Fellowship at Oxford (2005) and the Joseph O. Hirschfelder Prize (2003).

[1][2][3][4] Heller has also made contributions to methodology, suggesting the technique called "frozen Gaussians"—today the most widely used semiclassical initial value representation (IVR) method of wavepacket propagation.