Complex analysis in quantum mechanics

  • Why do we use complex numbers in quantum mechanics?

    A more general way to put it is to say that complex numbers are indispensable to describe (two-state) systems with more than two incompatible observables..

  • Quantum mechanics is deemed the hardest part of physics.
    Systems with quantum behavior don't follow the rules that we are used to, they are hard to see and hard to “feel”, can have controversial features, exist in several different states at the same time - and even change depending on whether they are observed or not.
  • They are of enormous use in applied maths and physics.
    Complex numbers (the sum of real and imaginary numbers) occur quite naturally in the study of quantum physics.
    They're useful for modelling periodic motions (such as water or light waves) as well as alternating currents.
The two teams show that, within a standard formulation of quantum mechanics, complex numbers are indispensable for describing experiments carried out on simple quantum networks. A basic starting point for quantum theory is to represent a particle state by a vector in a complex-valued space, called a Hilbert space.

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