On the possibility of an incorrect choice of a quantization volume

Abstract

The specific features of the choice of an incorrect quantization volume, based on the example of the preparation of a multimode quantum state in parametric scattering, are considered. A small definitely incorrect volume that substantially simplifies the solution of the problem is chosen; it is shown to yield correct results except for an insignificant phase factor, which is proved by comparison with a more accurate correct (in the sense of the quantization volume) solution. This provides hope that the solution of quantum problems can be considerably simplified, at least to a first approximation.