First quantization

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A first quantization of a physical system is a semi-classical treatment of quantum mechanics, in which particles or physical objects are treated using quantum wave functions but the surrounding environment (for example a potential well or a bulk electromagnetic field or gravitational field) is treated classically. First quantization is appropriate for studying a single quantum-mechanical system being controlled by a laboratory apparatus that is itself large enough that classical mechanics is applicable to most of the apparatus.

First quantization is the subject studied in most undergraduate quantum mechanics courses, and in which the Schrodinger Equation and Heisenberg matrix mechanics (together with bra-ket notation) are most simply applied. It may be contrasted with Second quantization, which includes quantum-mechanical uncertainty effects in all aspects of an experiment including the controlling fields and boundary conditions.