Text: A term applied to the transition from a description of a system of particles or fields in the classical approximation where canonically conjugate variables commute to a description where these variables are treated as noncommuting operators. In this transition, Poisson bracket relations among dynamical variables are replaced by commutation relations. So-called second quantization is the analogous treatment of a field, such as the electromagnetic field solution of Maxwell's equations, the wave-function solution of Schrodinger's equation, or the solution of Dirac's equation, with commutation relations imposed upon the field as the canonical coordinate and with the generalized momentum defined through the Lagrangian. The wave equation in the latter two cases resulted from the first quantization.

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Source: The Dynamic Theory of Life and Mind, Alexander, James B., Minneapolis, The Housekeeper Press, 1893. ,