A generalization of the canonical commutation relation and Heisenberg uncertainty principle for the orbital operators

Abstract

In this paper, the orbits of observable physical quantities of position and momentum operators at the states of quantum Hilbert spaces are created. Also the Hilbert space of finite orbits and the Fréchet–Hilbert space of all orbits are created and the orbital operators corresponding to these observable operators in these spaces of orbits are defined and studied. We call this process the orbitization, and the obtained model the orbital quantum mechanics. The orbitization process is compared with the quantization process. The generalization of well-known canonical commutation relations for orbital operators corresponding to the position and momentum operators is established. Also, the Heisenberg uncertainty principle for the orbital operators is proved and the question of achieving equality in the Heisenberg inequality is considered.