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Translation invariant states in quantum mechanics

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We give a complete description of the states of the C.C.R. algebra for a finite number of degrees of freedom which are invariant with respect to subgroups of the translation group of phase space. We make precise some well-known results of quantum mechanics such as Bloch theorem.

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Communicated by H. Araki

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Beaume, R., Manuceau, J., Pellet, A. et al. Translation invariant states in quantum mechanics. Commun.Math. Phys. 38, 29–45 (1974).

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