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In physics, quantization refers to the formulation of a classical
theory in the formalism of quantum physics. Even though classical physics stems from quantum theory, the build up of a quantum
theory is often made the other way around, starting from existing classical physics to derive the more fundamental quantum
counterpart. For instance one can speak of the quantization of the electromagnetic field.
Quantization in quantum theory is the taking of
discrete rather than continuous values for some physical quantities (e.g. the total energy of a black body). When a quantity can only take on integer
multiples of some base value, the smallest possible intervals between the discrete values are quanta. The size of the quanta typically varies from system to system, but the Planck constant usually playes a crucial role in it. Using wave functions and applying boundary
conditions on them often does quantization.
2nd quantization is a special
formalism of quantum theory suited to deal with variable number of particles. It pertains to quantum field theory and draws its name from a loose understanding of the formalism as
quantifying once more an already quantized theory. According to the formal explanation a quantized theory deals with operators and normal wave
functions, while second quantization makes also the wave functions operators, that makes the number of particles also
quantized, i.e. half an electron is not possible. In this sense second quantization is a full quantization.
It has been said that quantization is a mistery, but second quantization is a functor.
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