A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...

Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What ...

Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

Imaginary numbers might seem like unicorns and goblins — interesting but irrelevant to reality. But for describing matter at its roots, imaginary numbers turn out to be essential. They seem to be ...

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...