Physics – Quantum Physics
Scientific paper
2003-10-20
J.Math.Phys. 45 (2004) 3659-3675
Physics
Quantum Physics
15 pages, Accepted for publication in Journal of Mathematical Physics
Scientific paper
10.1063/1.1782671
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 non-unitary 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 quantum correspondence rule. It is possible to get transformation laws of wave function under Galilei transformation for any scalar potential. This generalizes mass superselection rule. There is also given a new and general interpretation of a momentum representation of 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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