New parameters of Non-commutativity in Quantum Mechanics

Abstract

At this paper, it is considered to find a way for defining non-commutative spaces by ordinary commutative ones and vice versa. A novel parameter which has not been considered so far is represented. This parameter describes equivalent spaces. Also, we searched concepts of these new parameters with one problem. Noncommutativity in total space is important here because it could explain more concepts. As we knew SW method (Seiberg-Witten) explained noncommutativity so here, we showed that it was not suitable for some conditions.in the end we considered Hamiltonian of free particle in new noncommutativity and we found concepts of new parameters.