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A first quantization of a physical system is a possibly semiclassical treatment of quantum mechanics, in which particles or physical objects are treated using quantum wave functions but the surrounding environment is treated classically.

However, this need not be the case. In particular, a fully quantum version of the theory can be created by interpreting the interacting fields and their associated potentials as operators of multiplication, provided the potential is written in the canonical coordinates that are compatible with the Euclidean coordinates of standard classical mechanics. First quantization is appropriate for studying a single quantum-mechanical system being controlled by laboratory apparatuses that are governed by classical mechanics, for example an old fashion voltmeter , a simple thermometer, a magnetic field generator, and so on.

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