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 ...

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 ...

Now, on to the subject of complex numbers. We have stayed away from this subject until now simply because we did not want to confuse things. Initially, it is easy to think of signals as “real valued.” ...