On the explicit-time-dependent invariance properties of quantum mechanical systems

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Abstract
We use the notion of split extension algebra to embody a given invariance algebra of a quantum mechanical system, a realization of which is known in terms of some variables, in a richer invariance algebra expressed in terms of the same variables. By applying this procedure to a free system of particles we show how to obtain the invariance under the Schrödinger algebra and we build a bigger invariance algebra which describes a system of noninteracting particles, for example the asymptotic states in a nonrelativistic scattering problem.

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