Abstract
We give a physical notion to all self-adjoint extensions of the operator id/dx in the finite interval. It appears that these extensions realize different nonunitary equivalent representations of CCR and are related to the momentum operator viewed from different inertial systems. This leads to the generalization of Galilei equivalence principle and gives a new insight into the quantum correspondence rule. It is possible to get transformation laws of the wave function under Galilei transformation for any scalar potential. This generalizes the mass superselection rule. There is also given a new and general interpretation of a momentum representation of the wave function. It appears that consistent treatment of this problem leads to the time-dependent interactions and to the abrupt switching-off of the interaction.
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