Complex Analysis explores the properties and applications of complex numbers and functions, emphasizing their geometric interpretations and analytical techniques.
Quantum mechanics is full of complex numbers! The wave function, which describes the state of a particle, is a complex-valued function.
The mathematics of quantum mechanics—like the Schrödinger equation—relies on complex analysis for solutions and predictions. Probabilities and physical observables are extracted from these complex wave functions.
Understanding atomic structure, lasers, and even how your phone works all depend on this deep math.
Solving the Schrödinger equation for an electron in a hydrogen atom.
Understanding interference patterns in a double-slit experiment using complex exponentials.