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 ...

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Introduces methods of complex variables, contour integration, and theory of residues. Applications include solving partial differential equations by transform methods, Fourier and Laplace transforms, ...

Bicomplex analysis, an extension of traditional complex analysis, investigates functions defined on bicomplex numbers – entities formed by a pair of complex units. This framework enriches classical ...

An international team of researchers shows through a concrete theoretical experiment that the prediction by standard complex quantum theory cannot be expressed by its real counterpart and ratifies its ...