100th anniversary of Schrödinger's equation

In early 1926, Erwin Schrödinger introduced his celebrated wave equation,

iℏ ∂ψ(x,t)/∂t = (−ℏ²/(2m) ∇² + V(x)) ψ(x,t)

motivated by the interplay between geometrical and wave optics, the least-action principle, and de Broglie's matter waves. By elevating Planck's constant ℏ into the dynamical law (rather than treating it only as a quantization constant) and placing the complex wavefunction ψ at center stage (with the imaginary unit i ensuring reversible time evolution), Schrödinger set the mathematical foundation of quantum theory. 

Very soon after its introduction, Born provided the mysterious function ψ(x,t) with an interpretation: |ψ(x,t)|² represents a probability density. This interpretation connected Schrödinger's reversible wave dynamics with intrinsically probabilistic measurement outcomes - fueling foundational debates from wave-particle duality to entanglement - while simultaneously delivering spectacular predictive power. 

Schrödinger's equation explained atomic spectra, enabled quantum chemistry and modern materials science, and underlies technologies from semiconductors and lasers to tunneling-based devices, while also seeding today's quantum information science. 

A century on, it remains a living tool - refined, approximated, and generalized - continuing to shape how we understand and engineer the physical world.

Text by Borivoje Dakic.

In 1906, Erwin Schrödinger registered for mathematics and physics at the University of Vienna. Among his professors were Franz Serafin Exner (1849–1926) and Friedrich Hasenöhrl (1874–1915). Hasenöhrl’s lectures on thermodynamics introduced Schrödinger to the emerging ideas on quantum theory, although this wouldn’t be his initial research focus. 

He wrote his dissertation in 1910 and, after a year of military service, became an assistant at Exner’s institute. In 1914, Schrödinger received his Habilitation and was briefly able to give his first lectures before being called up; he spent the First World War as an officer on Austria’s southern front. He then returned to the University of Vienna for another two years, before leaving Austria for most of his remaining academic career. Apart from a guest professorship in Innsbruck in 1950, Schrödinger only fully returned in 1956 as professor emeritus for a chair that the University of Vienna had founded specifically for him. 

Text by Helen Piel

The majority of Erwin Schrödinger's scientific legacy is now kept at the Austrian Central Library for Physics of the University of Vienna and partially included in the online exhibition on Erwin Schrödinger.

Digitised archival material is also available on the University's repository Phaidra.

What began 100 years ago as a mathematical description of the quantum world has since become the foundation of the most transformative technologies and industries shaping our lives. Devices such as computers, lasers, and magnetic resonance imaging all trace their roots back to quantum mechanics.

But today a new wave of quantum technologies is emerging. While earlier technologies relied on quantum effects in systems containing a large numbers of particles, recent advances have made it possible to control and manipulate individual quantum objects, enabling applications ranging from ultra-precise sensing and fundamentally secure communication to faster and more powerful computing.

Turning scientific breakthroughs into impact beyond the lab, however, requires more than equations. Researchers also need an understanding of markets and business, as well as access to the right network of innovation experts and investors to support this transition.

With the quantum innovation lab, the University of Vienna supports researchers and students in taking this step, helping them explore how their quantum research can evolve into viable products, companies and societal impact. In this way, the legacy of Schrödinger's equation continues not only in theory, but in innovations shaping the next century.

In this video, you can get an impression on the quantum innovation lab.

Text by Helene Hainzer