On the roles of complex numbers in the birth of quantum mechanics: Heisenberg vs. Schrödinger

by Ricardo Karam (University of Copenhagen)

Thursday 18 Jun 2026, 14:00 → 15:00 Europe/Zurich

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From the big bang to black holes, from elementary particles and the fundamental interactions that govern our universe to the world's largest and most complex scientific instruments, our knowledge of the world builds on modern physics. To make our current-best understanding available to all, we need to invest in educational research and bridge the gap between those who know science, those who teach science, and those who learn science. 

This month, we will discuss a paper by Ricardo Karam from the University of Copenhagen.

Abstract: 

The idea that complex numbers are essential for quantum mechanics is widespread in the physics community, although some would argue that it is a matter of calculation convenience. The issue has received significant attention recently, but what was the role played by complex numbers in the birth of quantum mechanics? In this seminar, this question will be addressed by contrasting how complex expressions were present (and justified) in the groundbreaking works of Heisenberg (1925) and Schrödinger (1926). In the matrix mechanics side, it will be shown that Heisenberg used different representations of Fourier series, real and complex, and that these choices were bound by a negotiation between mathematical convenience and physical interpretation. From the wave mechanics perspective, it will become clear how Schrödinger initially refused to accept a complex wave function and assigned physical meaning only to its real component.

Paper:

Karam, R. (2020). Schrödinger's original struggles with a complex wave function. American Journal of Physics, 88(6), 433-438. https://doi.org/10.1119/10.0000852